Find the domain of $f(x)=\sin ^{-1}(5 x)$
A) $[-5,5]$
B) $\left[-\frac{1}{5}, \frac{1}{5}\right]$
C) $[-1,1]$
D) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
E) $\left[-\frac{\pi}{10}, \frac{\pi}{10}\right]$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \sin^{-1}(5x)$ is determined by the input values of $5x$ that make the expression valid. Since the sine function (and its inverse) can only take values between -1 and 1, $5x$ must also be between -1 and 1. Solving for $x$ gives $-\frac{1}{5} \leq x \leq \frac{1}{5}$, which corresponds to choice B.

Find the Domain Of f(x)=sin⁡−1(5x)f(x)=\sin ^{-1}(5 x)f(x)=sin−1(5x) A) [−5,5][-5,5][−5,5] B) [−15,15]\left[-\frac{1}{5}, \frac{1}{5}\right][−51​,51​] C) [−1,1][-1,1][−1,1]

Find the Domain Of $f(x)=\sin ^{-1}(5 x)$ A) $[-5,5]$ B) $\left[-\frac{1}{5}, \frac{1}{5}\right]$ C) $[-1,1]$