Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 227: 81

Answer

(a) $f^{-1}(x)=x-2$ (b) See the image below.

Work Step by Step

(a) To find inverse of the function $f(x)=2+x$, we have to write it down in terms of $y$ and $x$ and then replace them by each other. And at last solve for $y$. So we have: $y=2+x$ Inverse: $x=2+y$ $y=x-2$ $f{-1}(x)=x-2$ (b) We can graph them using graphing calculator, or even simply take two arbitrary $x$ value to find corresponding $y$ value and graph it by connecting these points. See the image above.
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