Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises - Page 68: 75


Domain: $ -\frac{2}{3}\leq x\leq0$ Range: $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$

Work Step by Step

Since the $\sin^{-1}$ function can only accept values between $-1$ and $1$, $-1\leq 3x+1\leq1$ $-2\leq 3x\leq0$ $\therefore -\frac{2}{3}\leq x\leq0$ $g(x)$ like the standard $f(x)=\sin^{-1}(x)$ will produce values between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ as its inputs are the same (all real values between $-1$ and $1$). So its range is $-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}$
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