(Section 1.9: Inverses of One-to-One Functions) 1.9.13Example 9 (Checking an Inverse Function Formula; Revisiting Examples 6 and 7)Again, let fx()=x3+57on ±. Let gx=7x±53on ±. Check that g=f±1. § SolutionWe will verify that the compositions g±fand f±gare identity functions. Either check below is sufficient, becausefis one-to-one, and Rangef=Domg(each set is ±). If in doubt, do both checks. (See Footnote 1.)Check that g±fx=x, ±x²±
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Inverse function, Injective function, Inverse Function Formula