(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()=x2on ±. Then,fis a function, but it is notone-to-one on ±, as demonstrated by the figures below: Input-Output MachinePartial Arrow DiagramGraphFails HLT (Section 1.8) §• Also, fa=fc±a2=c2±a=±c, which is notequivalent to a=c, if c±0. If we solve the equation=9, or x2=9, we obtain twosolutions for x,namely3 and ±3. These are the twoanswers to the question, “Whose square is 9?”
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