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: 82

Answer

(a) $f^{-1}(x)=-2x+4$ (b) See the image below.

Work Step by Step

(a) To find inverse of the function we have to follow the next strategy: First write down the function in terms of $y$ and $x$, Then replace $y$ by $x$ and vice versa, At last solve the equation for $y$. We have $f(x)=2-\frac{1}{2}x$ $y=2-\frac{1}{2}x$ $x=2-\frac{1}{2}y$ $\frac{1}{2}y=2-x$ $y=2(2-x)$ $y=4-2x$ $f^{-1}(x)=-2x+4$ (b) We can sketch the graph of these functions using graphing calculator. See the image above.
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