Precalc0108to0109-page23

Precalc0108to0109-page23 - (Section 1.9: Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.13 Example 9 (Checking an Inverse Function Formula; Revisiting Examples 6 and 7) Again, let fx () = x 3 + 5 7 on ± . Let gx = 7 x ± 5 3 on ± . Check that g = f ± 1 . § Solution We will verify that the compositions g ± f and f ± g are identity functions. Either check below is sufficient, because f is one-to-one, and Range f = Dom g (each set is ± ). If in doubt, do both checks. (See Footnote 1.) Check that g ± f x = x , ± x ² ±
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