Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 230: 90a


$f^{-1} (x)=y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$

Work Step by Step

Let $x$ be exhaust temperature and $y$ be the percent load. We have $y=0.03x^2+245.50; 0 \lt x \lt 100$ To compute the inverse, we will have to interchange $x$ and $y$. $x=0.03y^2+245.50; 245.50 \lt x \lt 545.50$ Re-write as: $ x-245.50=0.03; 245.50 \lt x \lt 545.50$ or, $y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$ Replace $y$ with $f^{-1} (x)$. $f^{-1} (x)=y=\sqrt {\dfrac{x-245.50}{0.03}}; 245.5 \lt x \lt 545.5$
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