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CA_GPS_21

# CA_GPS_21 - 1 f 1 Determine whether the given function is...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 21 2.7 INVERSE FUNCTIONS Class Time: ____________ Date: __________ Useful Guidelines: * One-to-one function: A function whose inverse is also a function. [If 2 1 x x ! , then ) ( ) ( 2 1 x f x f ! ] * Horizontal-line test : If every horizontal line intersects the graph of f in at most one point , then f is one-to-one . * The graph of a function f and its inverse 1 ! f are symmetric with respect to the line x y = . * To find the inverse, ) ( 1 x f ! , of a one-to-one function: (1) Let ) ( x f y = (2) Interchanging the variables x and y (3) Solve for y and replace y by ) ( 1 x f ! (4) Check the result by showing that x x f f = ! )) ( ( 1 and x x f f = ! )) ( ( 1 * To find the range of a one-to-one function f , find the domain of the inverse function 1 ! f . [Domain of f = Range of 1 ! f ; Range of f = Domain of
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Unformatted text preview: 1 ! f .] 1. Determine whether the given function is one-to-one. If it is one-to-one, find the inverse. [Hint: Check to see if there are ordered pairs with different first coordinates and the same second coordinate. If there are, the function is not one-to-one. We can find its inverse by interchanging the x- and y-coordinates in each ordered pair.] (a) )} 6 , 9 ( ), 4 , 7 ( ), 2 , 3 ( ), 1 , 2 {( ! (b) )} 16 , 4 ( ), 4 , 2 ( ), , ( ), 4 , 2 {( ! 2. Use the graph to determine whether the function is one-to-one. [Hint: use Horizontal-line test] (a) 3 ) ( x x f = (b) 2 ) ( x x f = 3. In the following problems, determine whether the function f is one-to-one. If it is, find the inverse of each function. (a) 3 ! x (b) 2 3 ! x...
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