CA_GPS_22 - f , find the domain of the inverse function 1 !...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 22 2.7 INVERSE FUNCTIONS II 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 (read as f inverse) 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
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Unformatted text preview: f , find the domain of the inverse function 1 ! f . [Domain of f = Range of 1 ! f ; Range of f = Domain of 1 ! f .] 1. Given x x f 50 ) ( = and 50 ) ( x x g = , find the following: a) )) ( ( x g f b) )) ( ( x f g Determine whether the pair of functions f and g are inverses of each other. 2. If 18 50 ) ( 3 ! = x x f and 3 50 18 ) ( + = x x g , find the following: a) )) ( ( x g f b) )) ( ( x f g Determine whether f(x) and g(x) are inverse functions. 3. Determine the function is one-to-one. If it is one-to-one, find a formula for its inverse and check the result by showing that x x f f = ! )) ( ( 1 and x x f f = ! )) ( ( 1 x x f 7 ) ( =...
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