College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 90

Answer

Not one-to-one.

Work Step by Step

We are given: $g(x)=2-2x+x^{2}$ We factor by completing the square: $2-2x+x^{2}$ $x^2-2x+2$ $(x^{2}-2x+1)+1$ $(x-1)^{2}+1$ This function is not one-to-one because it fails the horizontal line test (it is a shifted parabola, which is an even function.) We can show that this function has the same $y$ value for two $x$ values: $g(0)=2-2*0+0^2=2$ $g(2)=2-2*2+2^2=2-4+4=2$ Thus the function is not one-to-one.
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