# section7_1 - Section 7.1 Inverse functions A function f is...

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Section 7.1 Inverse functions

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A function f is invertible if It can be reversed. You can find an inverse function f -1 which undoes whatever f does.
Which functions are invertible?

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Which functions are invertible? f: A B is invertible iff f is one-to-one on A distinct inputs give different outputs: If x 1 x 2 , then f(x 1 ) f(x 2 )
From the formula of f: check f(x 1 )=f(x 2 ) x 1 =x 2 From the derivative of f: f’(x) does not change sign From the graph of f: horizontal line test for f ( x ) = x , x 1 = x 2 ! x 1 = x 2 Mvc,b.cvb f’(x)>0 for all x f’(x)<0 for all x not one-to-one

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Question The function y=(x 3 +7x) 133 is invertible. True False
Question The function f(x)=(x 3 +7x) 133 is invertible. True False f’(x)=133 (x 3 +7x) 132 (3x 2 +7) is zero at a single point, and is otherwise positive, so f is increasing.

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Question No even function is invertible (in its full domain). True False
Question No even function is invertible (in its full domain). True False If f is even, then f(x)=f(-x).

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