Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 35: 20

Answer

$(-\infty,1]$ and any interval included in it $[1,\infty)$ and any interval included in it

Work Step by Step

We are given the function: $f(x)=x^2-2x+8=(x^2-2x+1)-1+8=(x-1)^2+7$ We graph the function. The vertex is $(1,7)$. The domain of $f$ is $(-\infty,\infty)$. The range of $f$ is $[7,\infty)$. Using the Horizontal Line Test we notice that any horizontal line in the range of the function intersects the graph in two points. Therefore the function $f$ doesn't have an inverse on $(-\infty,\infty)$. We determine a restriction of the function's domain on which the function has an inverse: $(-\infty,1]$ and any interval included in it $[1,\infty)$ and any interval included in it
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