Precalc0108to0109-page14

Precalc0108to0109-page14 - (Section 1.9: Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.4 Example 1 demonstrates that, in going from a function to its inverse (if it exists), inputs and outputs switch roles . This is a key theme. “Input-Output” Properties of Inverse Functions (can also be taken as the Definition of an Inverse Function) If f has an inverse function f ± 1 , then fa () = b ± f ² 1 b = a . • That is, a , b ± f ² b , a ± f ³ 1 . Domain and Range of Inverse Functions If f has an inverse function f ± 1 , then: Dom f = Range f ± 1 , and Dom f ± 1 = Range f . That is, the domain of one function is the range of the other. Example 2 (Inverse Functions: Verification, Domain, and Range) a) Let fx = x 3 on ± . Find f ± 1 , and verify that it is the inverse of f . b) Let gx = x 3 on 0, 2 ± ² ³ ´ . Find g
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