Precalc0108to0109-page22

Precalc0108to0109-page22 - (Section 1.9: Inverses of...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.12 Step 3 : Solve for y . 7 x = y 3 + 5 Multiplied both sides by 7 () 7 x ± 5 = y 3 Subtracted 5 from both sides 7 x ± 5 3 = y Cubed both sides WARNING 3 : Squaring both sides of an equation may or may not yield an equivalent equation. y = 7 x ± 5 3 • Compare these steps with Steps 3*, 2*, and 1* in Example 6. Step 4 : Replace y with f ± 1 x , if we obtain a function. f ± 1 x = 7 x ± 5 3 f ± 1 is a function, because f was one-to-one . Step 5 : If necessary, impose restrictions and ensure that Dom f = Range f ± 1 , and Dom f ± 1 = Range f .
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