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Q.
The domain of $cosh^{-1} \, 5x$ is
Relations and Functions
Solution:
$
\begin{array}{l}
\cosh ^{-1} x=\log \left[x+\sqrt{x^{2}-1}\right] \\
\cosh ^{-1} 5 x=\frac{1}{5} \log \left[x+\sqrt{x^{2}-1}\right]
\end{array}
$
Range of $\log$ is from 1 to $\infty$ as $x>0$ for $\cosh ^{-1} x$ to be defined
$
\therefore \text { range is }=\left[\frac{1}{5}, \infty\right]
$