(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)Iffhas an inverse function f±1, then fa()=b±f²1b=a. • That is, a,b±f²b,a±f³1. Domain and Range of Inverse FunctionsIffhas an inverse function f±1, then: Domf=Rangef±1, and Domf±1=Rangef. That is, the domainof one function is the rangeof the other. Example 2 (Inverse Functions: Verification, Domain, and Range)a) Let fx=x3on ±. Find f±1, and verify that it is the inverse off. b) Let gx=x3on 0, 2±²³´. Find g
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