Precalc0108to0109-page16

Precalc0108to0109-pa - (Section 1.9 Inverses of One-to-One Functions 1.9.6 Example 3(A Function that is Not One-to-One Unrestricted Squaring

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(Section 1.9: Inverses of One-to-One Functions) 1.9.6 Example 3 (A Function that is Not One-to-One: Unrestricted Squaring Function) Let fx () = x 2 on ± . Then, f is a function, but it is not one-to-one on ± , as demonstrated by the figures below: Input-Output Machine Partial Arrow Diagram Graph Fails HLT (Section 1.8) § • Also, fa = fc ± a 2 = c 2 ± a c , which is not equivalent to a = c , if c ± 0 . If we solve the equation = 9 , or x 2 = 9 , we obtain two solutions for x , namely 3 and ± 3 . These are the two answers to the question, “Whose square is 9?”
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This document was uploaded on 12/29/2011.

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