Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 2 - Functions - 2.1 Input and Output - Exercises and Problems for Section 2.1 - Exercises and Problems - Page 75: 5


(a) $g(0)=-\frac{1}{2}$ (b) $t=-1$

Work Step by Step

(a) Use $t=0$ to get $g(0)=\frac{1}{0+2}-1=\frac{1}{2}-1=\frac{1}{2}-\frac{2}{2}=-\frac{1}{2}$. (b) Use the fact that $g(t)=0$ for some $t$ to get $$\frac{1}{t+2}-1=0$$ Add $1$ to both sides to get $$\frac{1}{t+2}=1$$ Multiply both sides of the equation by $t+2$ to get $1=1(t+2)=t+2$. Finally, subtract $2$ from each side to get $$t=1-2=-1$$.
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