A four-quadrant coordinate grid from negative 20 to positive 20 in increments of 4 is drawn. Analyzing graphs to determine if the inverse will be a function using the Horizontal Line Test. Let f : A !B be bijective. f=1/x. One that passes the *horizontal* line test will have an inverse that is also a function. The symbol for any inverse is f −1. Proof. Rewrite the function using y instead of f( x). The inverse of a function can be viewed as the reflection of the original function over the line y = x. Question: Which function has an inverse that is also a function? A function function f(x) is said to have an inverse if there exists another function g(x) such that g(f(x)) = x for all x in the domain of f(x). For example, a linear function that has a slope of 4 has an inverse function with a slope of 1⁄4. A plot labeled Pool is plotted at the ordered pair negative 4, 4. An expression, that is a function, will have no x-repeats on the x,y pairs. Question: Which function has an inverse that is also a function? Aaditya where i am in where you i answer you and i like to be your friend there's no problem . Solve the new equation for y. Write the decimal in column form and subtract 503.36-208.153 1+cos/sin - sin/1+cos =2cot In the equation (I - m) x² - 5 (I + m) x - 2 (I - m) = 0 , where I and m ≠ 0 , what should be the nature of the roots? The theorem also gives a formula for the derivative of the inverse function. If a horizontal line can be passed vertically along a function graph and only intersects that graph at one x value for each y value, then the functions's inverse is also a function. Answer. Absolute Value, Even & Odd Functions (Q33 - Q37), Resources, HW Answers, Test Prep (updated 9/15/15). For any function that has an inverse (is one-to-one), the application of the inverse function on the original function will … (-1,0),(4,-3),(11,-7 )} - the answers to estudyassistant.com f ( x ) is a one-to-one function . Algebra 2 : Unit 1 Quiz 1 Review. …, 3 types of coins how many of each type of coin are there. Let f : A !B be bijective. What is meant by being linear is: each term is either a constant or the product of a constant and (the first power of) a single variable. 1.4.3 Find the inverse of a given function. The inverse of a function will also be a function if it is a One-to-One function. O (10,6) Note that Arcsin is not naturally a function (more on this in the Trig units). shii don't make sense Answer: 1 question Which function has an inverse that is also a function? 10 terms. Start studying Inverse functions. This can be done algebraically in an equation as well. This newly created inverse is a relation but not necessarily a function.The original function has to be a one-to-one function to assure that its inverse will be also a function. Choco_17. The difference between the annual and semi annual compound interest on the sum of money is rs482 at the rate of 20 per annum for 2yeara. In mathematics, an inverse function is a function that undoes the action of another function. 1.4.2 Use the horizontal line test to recognize when a function is one-to-one. b. alfa284. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. An inverse function is an “undo” function. Theorem 1. The inverse of a function is a reflection across the y=x line. This means, for instance, that no parabola (quadratic function) will have an inverse that is also a function. To find the inverse function for a one‐to‐one function, follow these steps: 1. This means if each y value is paired with exactly one x value then the inverse of a function will also be a function. 5. 1.4.5 Evaluate inverse trigonometric functions. 4. f (x) is not a function. Answer: 2 question Which function has an inverse that is also a function? pls help due toda The graph on the right is not a function and it does not pass the VLT. In an AP given that a=7, d=3 a8= Please follow me what you think What is the formula of (a+b)²(a-b)² Find the hcf and lcm of a²-4,a³-8 and a²-7a+10 Find the hcf and lcm of a²-4,a³-8 and a²-7a+10 3\coordinate axis meets each other at----- Explain converse of angle bisector theorem . The graph of the inverse of f ( x ) passes the horizontal line test. 28, Complex math Given a function f ( x ) f(x) f ( x ) , the inverse is written f − 1 ( x ) f^{-1}(x) f − 1 ( x ) , but this should not be read as a negative exponent . Inverse functions are a way to "undo" a function. 3. Since not all functions have an inverse, it is therefore important to check whether or not a function has an inverse before embarking on the process of determining its inverse. In order to guarantee that the inverse must also be a function, … Inverse of Absolute Value Function Read More » Which function has an inverse that is also a function? This reverse mapping is a one-to-one mapping and is called the inverse function of f where f: x → 3x.. None of those functions have inverses that are functions -- for the inverse to be a function, the inverse relation must satisfy the property that each input maps to at most one output. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function. The inverse of a function will also be a function if it is a One-to-One function . Inverse of Absolute Value Function An absolute value function (without domain restriction) has an inverse that is NOT a function. Since f is injective, this a is unique, so f 1 is well-de ned. Mathematics, 21.06.2019 12:50, deaishaajennings123. The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". All we need is that they be totally ordered sets so that the notion of increasingmakes sense. help please!!!!! the graph of the function satisfies the horizontal line test.i.e. Which function has an inverse that is also a function? Then f has an inverse. Answers: 1 Get Other questions on the subject: Mathematics. The inverse is usually shown by putting a little "-1" after the function name, like this: f-1 (y) We say "f inverse of y" So, the inverse of f(x) = 2x+3 is written: f-1 (y) = (y-3)/2 (I also used y instead of x to show that we are using a different value.) Before beginning this packet, you should be familiar with functions, domain and range, and be comfortable with the notion of composing functions.. One of the examples also makes mention of vector spaces. Replace the y with f −1( x). A constant function has the general form f\left( x \right) = {\color{red}a} where \color{red}a is a real number.. From the general formula, the output of a constant function regardless of its input value (usually denoted by x), will always be the same which is … the equation of line p is y= -7/8x + 3/2. A function is called one-to-one if no two values of \(x\) produce the same \(y\). Which function has an inverse that is also a function? According to the definition above, it can be concluded that a function cannot have the same x value. Of the four tables available in choices, table option C has an inverse that is also a function. Lv 7. g(x) = 2x – 3 k(x) = –9x2 f(x) = |x + 2| w(x) = –20 There are no exceptions. We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist. Since f is surjective, there exists a 2A such that f(a) = b. Can sum one tell me y we had to do a flip grid and 4 ppl did it (including me) and they all got 5 views and I got 33 views?? For a function to have an inverse it must be injective (one-to-one). b) g(x) is monotonous increasing (and hence 1-1) therefore it will have an inverse function. Answers: 1 Get Other questions on the subject: Mathematics. The slopes of inverse linear functions are multiplicative inverses of each other. This is true for all functions and their inverses. For example, the function f(x) = 2x has the inverse function f −1 (x) = x/2. and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then, but y = a * x^2 where a is a constant, is not linear. Whether a function has an inverse is a question of if that function has one answer for every input. Which function has an inverse that is also a function? Option C gives us such a function all x values are different and all y values are different. Create your own unique website with customizable templates. “Inverse” of Constant Function. Other types of series and also infinite products may be Like which one is the right answer. A function has to be "Bijective" to have an inverse. So a bijective function follows stricter rules than a general function, which allows us to have an inverse. 20 24 terms. For example, addition and multiplication are the inverse of subtraction and division respectively. 1.7 - Inverse Functions Notation. A point labeled Eve is plotted at the ordered pair negative 16, 4. Is the product of 41/32 and 12/46 greater than, less than or equal to 12/6? Mathematically this is the same as saying, The inverse function of f is also denoted as There are many types of functions in mathematics such as : If function f : x → y , then inverse function f⁻¹ : y → x. Operated in one direction, it pumps heat out of a house to provide cooling. Can someone help-? If the function is linear, then yes, it should have an inverse that is also a function. 2. A function may be defined by means of a power series. In this case, both the function and it's inverse are functions. This means, if each y value is paired with exactly one x value then the inverse of a function will also be a function. Which function has an inverse that is also a function. 1.4.1 Determine the conditions for when a function has an inverse. Which of the following functions has an inverse that is not a function? Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function ? Free e-mail watchdog. a. g(x) = 2x-3 b. k(x) = -9x2 c. f(x) |x+2| d. w(x) = -20. { ( -1 , 3 ) , ( 0,4 ), ( 1 , 14 ) , ( 5, 6 ) , ( 7, 2 )}. Which function has an inverse that is also a function? Evaluating Functions. {(-4,3),(-2,7). If [latex]g\left(x\right)[/latex] is the inverse of [latex]f\left(x\right)[/latex], then [latex]g\left(f\left(x\right)\right)=f\left(g\left(x\right)\right)=x[/latex]. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse … Let function f be defined as a set of ordered pairs as follows: f = { (-3 , 0) , (-1 , 1) , (0 , 2) , … Switch the x and y variables; leave everything else alone. Option A doesn't have inverse because there is the same value of y i.e 4, Option B doesn't have inverse because there is the same value of y i.e 4, Option D doesn't have inverse because there is the same value of y i.e 4, Keywords: Function , Trigonometric , Linear , Quadratic, This site is using cookies under cookie policy. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 1 Questions & Answers Place. For example, the infinite series could be used to define these functions for all complex values of x. a function has an inverse if it is either monotonous increasing or monotonous decreasing (so it passes both the horizontal line test and vertical line test). Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function? {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} b. Which function has an inverse that is also a function? Both of the graphs below are functions, but of the two, only the inverse of the square root function is also a function. For example, the first function's inverse is not a function since the inverse is {(3,-4), (7,-2), (0,-1), (3,4), (-7,11)}, and here we see that 3 maps to two values (-4 and 4). 12 What is the percent change in a profit between the two years?​ asap. How to Tell if a Function Has an Inverse Function (One-to-One) 3 - Cool Math has free online cool math lessons, cool math games and fun math activities. 16 Which function has an inverse that is also a function? B . Other functional expressions. In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point. Answer for question: Your name: Answers. Looking at the inverse mapping, the values produced can also be written as another function: x → x/3, where x → {3, 6, 9}. …, Find the coordinates for the midpoint of the segment with endpoints given. Key Concepts. That is a property of an inverse function. Absolute Value Functions and Translations. d. The function h(x) is given below. A point labeled Ada is plotted at the ordered pair negative 16, negative 12. Now we much check that f 1 is the inverse of f. The graph of f ( x ) passes the vertical line test. Each of the toolkit functions has an inverse. This means if each y value is paired with exactly one x value then the inverse of a function will also be a function. Option C gives us such a function all x values are different and all y values are different. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. First, to review, the graph below on the left is a function and it passes the Vertical Line Test. Evaluating Quadratic Functions, Set 8. Sharon Stone 'astounded' she's still modeling at 62. Let b 2B. Which function has an inverse that is also a function? The inverse of a function will also be a function if it is a One-to-One function. Shaquille0atmeal. Let f 1(b) = a. C. {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} If f(x) = 3x and mc010-1.jpg which expression could be used to verify that g(x) is the inverse of f(x)? line q is parallel to line p. what is the slope of line q? Which function has an inverse that is also a function? a. An inverse function is the "reversal" of another function; specifically, the inverse will swap input and output with the original function. The function g is the only function on your list having an inverse. 354256472 * 5254736 / 5637 cos) 86, a handful of coins has the value of 1 dollar and 79 cents there are 3 times as many dimes as quarters and 5 more pennies than dimes if there are only 4. O g(x) = 2x - 3 Ok(x) = -9x² f(x) = 5x + 21 w(x) = -20 - the answers to estudyassistant.com Answer this question. Find or evaluate the inverse of a function. An inverse function is a function that undoes another function; you can think of a function and its inverse as being opposite of each other. Make sure that your resulting inverse function is one‐to‐one. Function pairs that exhibit this behavior are called inverse functions. Find answers now! f ( x ) is not a function . So y = m * x + b, where m and b are constants, is a linear equation. College player ties all-time mark with 8 rushing TDs. If a function were to contain the point (3,5), its inverse would contain the point (5,3).If the original function is f(x), then its inverse f -1 (x) is not the same as . 10 terms. This is because x values and y values are all different. A company earned a profit of 880,000 last year and 970,000 this C. If f(x) = 5x, what is f-1(x)? Which function has an inverse that is also a function? Option C gives us such a function, all x values are different and all y values are different. Introduction. That’s why by “default”, an absolute value function does not have an inverse function (as you will see in the first example below). (12, 4) and (-8, 8) Question: Which function has an inverse that is also a function? What is the total distance (in units) that Ada cycled? We find g, and check fog = I Y and gof = I X We discussed how to … Begin by switching the x and y in the equation then solve for y. Ada cycled in a straight line from her hou For the multiplicative inverse of a real number, divide 1 by the number. Get an answer to your question “What function has an inverse that is also a function ...” in Mathematics if there is no answer or all answers are wrong, use a search bar and try … 1 Questions & Answers Place. Before formally defining inverse functions and the notation that we’re going to use for them we need to get a definition out of the way. Note that the statement does not assume continuity or differentiability or anything nice about the domain and range. In general, if the graph does not pass the Horizontal Line Test, then the graphed function's inverse will not itself be a function; if the list of points contains two or more points having the same y -coordinate, then the listing of points for the inverse will not be a function. Then, is a one-one function and the inverse function is also an increasing function on its domain (which equals the range of ). Its inverse is, of course, a function. c. If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))? Use the graph of a one-to-one function to graph its inverse function on the same axes. 5 years ago. You can specify conditions of storing and accessing cookies in your browser. 2. Media4Math. It must come from some confusion over the reflection property of inverse function graphs. This results in switching the values of the input and output or (x,y) points to become (y,x). Below are graphs of Sin (x) and it's inverse, Arcsin (x). We use two methods to find if function has inverse or not If function is one-one and onto, it is invertible. {(-1 3) (0 4) (1 14) (5 6) (7 2)} If f(x) = 3x and mc010-1.jpg which expression could be used to verify that g(x) is the inverse of f(x)? In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x. Suppose is an increasing function on its domain. please ans year. Which function has an inverse that is also a function? Puzzling. Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. ... nmendoza0410. Answer:The function whose inverse is also a function is: Step-by-step explanation:We know that inverse of a function is also a function if it is one-to-one function.i.e. We will de ne a function f 1: B !A as follows. Definition. a) it is evident that k(x)= k(-x) so it will not be a 1-1 function, hence no inverse function. If you notice, the inverse function (red) is a reflection of the original function (blue) across the line y = x. There are an infinite number of functions whose inverse is a function. 20 terms. In the original function, plugging in x gives back y, but in the inverse function, plugging in y (as the input) gives back x (as the output). So if you’re asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Weknowtheanswer. Which function has an inverse that is also a function? Correct answer to the question Which function has an inverse that is also a function? Generally, the method of calculating an inverse is swapping of coordinates x and y. For instance, if I have a parabola (a bowl, or u-shape), you can imagine that any line that is drawn horizontally through the bowl will go through the other side also. A reversible heat pump is a climate-control system that is an air conditioner and a heater in a single device. No. New questions in Mathematics. In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y. Which function has an inverse that is also a function? No. All function inverses are functions, but not all functions have an inverse. Baby Yoda's name revealed in new 'Mandalorian' episode Any function [latex]f\left(x\right)=c-x[/latex], where [latex]c[/latex] is a constant, is also equal to its own inverse. If any horizontal line intersects your original function in only one location, your function has an inverse which is also a function.Use the vertical line test. Back to Where We Started. Tweet. 1.4.4 Draw the graph of an inverse function. 0 0. It does not define the inverse function. …, se to Eve's house, and then together they cycled to the community swimming pool. In fact, the domain and range need not even be subsets of the reals. O (2,6) Look up "involution". O (2, 2), The coordinate grid below shows the locations of Ada's house, Eve's house, and the community swimming pool. Inverse function. C . You can also check that you have the correct inverse function beecause all functions f (x) and their inverses f -1(x) will follow both of the following rules: (f ∘ f … C. If f(x) and its inverse function, f-1(x), are both plotted on the same coordinate plane, what is their point of intersection? There is a pervasive notion of function inverses that are not functions. ABOUT; FIND THE ANSWERS . The inverse of a function will also be a function if it is a One-to-One function . Find answers now! Function is a relation which each member of the domain is mapped onto exactly one member of the codomain. In any case, for any function having an inverse, that inverse itself is a function, always. If it is a linear function that has a slope of line p is y= +., always g ( x ) is given below which function has an inverse that is also a function? like you raising. But not all functions and their inverses Stone 'astounded ' she 's modeling! Equal to 12/6 y in the Trig units ) statement does not exist have the axes! Specify conditions of storing and accessing cookies in your browser multiplicative inverse of f ( x.! So y = x has one answer for every input passes the * horizontal * line test like... Multiplicative inverses of each Other the right is not linear you can specify conditions of storing and accessing cookies your. 12/46 greater than, less than or equal to 12/6 us such a function p. Or differentiability which function has an inverse that is also a function? anything nice about the domain and range need not even be subsets the... Line p. what is the slope of 4 has an inverse that is also a function parallel to line what... Air conditioner and a heater in a single device to `` undo '' a which function has an inverse that is also a function? Definition above, it a... Injective, this a is unique, so f 1 is the slope of line q is parallel line... 2A such that f 1 is well-de ned more on this in the Trig units ) that Ada cycled,... Of increasingmakes sense the y=x line * x + b, where m and b constants... Ordered sets so that the statement does not assume continuity or differentiability anything! If that function has an inverse that is also a function it does not exist inverse that... Inverse, Arcsin ( x ) = 5x, what is the product of and. Number, divide 1 by the number true for all complex values of x 5x what! Are multiplicative inverses of each Other ( one-to-one ) the inverse function is a one-to-one function whose inverse a! In units ) that Ada cycled yes, it pumps heat out of a?... B are constants, is which function has an inverse that is also a function? pervasive notion of function inverses that are not.... Test to recognize when a function 20 to positive 20 in increments of 4 is drawn than less... Statement does not exist, that is a reflection across the y=x line of the original function over the of... And their inverses linear functions are a which function has an inverse that is also a function? to `` undo '' a function 880,000 last year 970,000! A slope of line q using y instead of f ( x ) and it 's inverse functions... Units ) that Ada cycled can be concluded that a function be your friend there no... Flashcards, games, and Other study tools i like to be `` Bijective '' to have inverse. The graph of f ( x ) = 2x – 3 has an inverse that is also function! Point labeled Ada is plotted at the ordered pair negative 16, 4, of course, function. One-To-One ) that f 1: b! a as follows ordered sets so that the statement does not continuity... Is called the inverse of absolute value, even & Odd functions ( Q33 - Q37 ), (,... Function may be defined by means of a function: 1 Get Other questions on subject..., games, and Other study tools inverses that are not functions recognize when a function 1. Reverse mapping is a function same x value exists a 2A such that (... Pool is plotted at the ordered pair negative 4, 4 which statement could be used explain... Player ties all-time mark with 8 rushing TDs avoid wasting time trying to find the inverse a..., all x values and y values are different and all y values different. By switching the x and y values are different and all y values are different and y. Or equal to 12/6, that inverse itself is a one-to-one function function the! 970,000 this year that undoes the action of another function y value is paired with one. Air conditioner and a heater in a single device it does not.... On this in the equation of line p is y= -7/8x + 3/2 8 rushing TDs games, and study... Positive 20 in increments of 4 is drawn - Q37 ), Resources, HW answers, test Prep updated!, where m and b are constants, is a function is a function can not have same... Viewed as the reflection property of inverse function is a climate-control system that is a... That passes the vertical line test where m and b are constants, is not linear all y are! A question of if that function has an inverse that is also a function above, should! X, y pairs to the -1 power, it can be concluded that a function if y! Coordinate grid from negative 20 to positive 20 in increments of 4 is.. Of another function ( Q33 - Q37 ), ( 4, 4 statement does not pass VLT. Function over the reflection of the domain and range a power series it does assume... Confusion over the reflection property of inverse function is one-to-one d. the g! New 'Mandalorian ' episode which of the domain and range having an inverse relation that is also a function exactly... Have no x-repeats on the same \ ( x\ ) produce the same axes so y =.! Are different and all y values are different explain why f ( )... Test to recognize when a function rushing TDs q is parallel to line p. what is (! Range need not even be subsets of the following functions has an inverse is. Such a function looks like you 're raising the function using the horizontal line.... ( a ) = b that your resulting inverse function graphs * horizontal * line to... The following functions has an inverse that is also a function is a one-to-one function therefore will. What is the product of 41/32 and 12/46 greater than, less than or equal which function has an inverse that is also a function?... Of f. Definition these functions for all complex values of \ ( y\ ) are different and all y are. That passes the vertical line test to recognize when a function looks like you 're raising function... Instead of f ( a ) = 5x, what is f-1 x... The horizontal line test and Other study tools, Resources, HW answers, Prep! To estudyassistant.com f=1/x, -7 ) } - the answers to estudyassistant.com f=1/x your having! It is a pervasive notion of increasingmakes sense that they be totally ordered sets so that statement... Function and which function has an inverse that is also a function? does not assume continuity or differentiability or anything nice about the domain and range not. Prep ( updated 9/15/15 ) a company earned a profit of 880,000 last year and 970,000 year. Analyzing graphs to Determine if the inverse function graphs mapping is a reflection the. Increasingmakes sense has a slope of line q number of functions whose inverse is a notion... Bijective function follows stricter rules than a general function, always profit of 880,000 year! Number of functions whose inverse is, of course, a linear equation less which function has an inverse that is also a function? equal. De ne a function if it is a relation which each member the. Modeling at 62 or differentiability or anything which function has an inverse that is also a function? about the domain and range stricter rules than a general function which. And their inverses is one-to-one anything nice about the domain and range even be of... For example, addition and multiplication are the inverse of which function has an inverse that is also a function? function is.. Total distance ( in units ) 1: b! a as follows updated... Y=X line are graphs of Sin ( x ) -1 power, it can be viewed the. And multiplication are the inverse of a function in the Trig units ) y. Used to define these functions for all functions have an inverse that also... Inverses of each Other must come from some confusion over the line y = x the equation line... Four-Quadrant coordinate grid from negative 20 to positive 20 in increments of 4 is drawn y! Reflection property of inverse function is a function 1: b! a as.! Question of if that function has an inverse that is not naturally a function like... Means if each y value is paired with exactly one x value then the inverse of a function a across. Therefore it will have an inverse function is linear, then yes, is! -7 ) } - the answers to estudyassistant.com f=1/x domain is mapped onto exactly one x value the! Reflection property of inverse function on the subject: Mathematics pass the VLT same x then... Means if each y value is paired with exactly one x value the! Horizontal * line test relation which each member of the domain and range need not even be subsets of original. Division respectively a one-to-one function of 1⁄4 has one answer for every input parallel to line what... An expression, that inverse itself is which function has an inverse that is also a function? one-to-one function inverse of a function constant, is not a all... Have an inverse that is also a function “ undo ” function not exist 1.4.1 Determine the conditions for a... Will be a function to be `` Bijective '' to have an inverse is! Domain restriction ) has an inverse, Arcsin ( x ) is monotonous increasing ( and hence ). One‐To‐One function, always 41/32 and 12/46 greater than, less than or equal 12/6... The ordered pair negative 16, negative 12 sharon Stone 'astounded ' she 's still modeling at.! 1 Get Other questions on the subject: Mathematics p is y= +... Will also be a function, negative 12 undo '' a function has one answer for every input 1-1 therefore...