Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises: 21

Answer

The inverse function is $$F=\frac{9}{5}C+32.$$ The domain of this function is $$[-273.15,\infty).$$

Work Step by Step

To find the inverse function we have to express $F$ in terms of $C$. To do so, we solve the equation $$C=\frac{5}{9}(F-32)$$ for $F$. This yields $$F-32=\frac{9}{5}C\Rightarrow F=\frac{9}{5}C+32.$$ This formula says what the temperature is in Fahrenheit when we know the temperature in Celsius. The domain of $F$-function is the same as the range of $C$-function which is $C=\frac{5}{9}(F-32),\quad F\geq-459.67$ giving $$C\geq\frac{5}{9}(-459.67-32)=-273.15$$ so the domain of the function $F=\frac{9}{5}C+32$ is $[-273.15,\infty).$
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