Precalc0108to0109-page20 - (Section 1.9 Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.10 PART E: FINDING FORMULAS FOR INVERSE FUNCTIONS If f is a one-to-one function , and if its formula can be expressed algebraically , then we should be able to find a formula for f ± 1 . Conceptual Approach to Finding the Inverse of a One-to-One Function f To determine f ± 1 , we need to invert (or “ undo ”) the steps applied by f in reverse order (WARNING 2 ) . (See the Exercises.) • Also, if necessary, impose restrictions and ensure that Dom f () = Range f ± 1 , and Dom f ± 1 = Range f . (See Example 10.) TIP 1 : Similarly, when dressing, you put on your socks before your shoes, but, when undressing, you remove your shoes before your socks. Example 6 (Conceptual Approach to Finding an Inverse)
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