Mark (√) against the correct answer in the following: Let $f(x)=\cos ^{-1} 2 x$. Then, $\operatorname{dom}(f)=?$ A. $[-1,1]$ B. $\left[\frac{-1}{2}, \frac{1}{2}\right]$ C. $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$ D. $\left[\frac{-\pi}{4}, \frac{\pi}{4}\right]$

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Mark (√) against the correct answer in the following: Let $f(x)=\cos ^{-1} 2 x$ . Then, $\operatorname{dom}(f)=?$
A. $[-1,1]$
B. $\left[\frac{-1}{2}, \frac{1}{2}\right]$
C. $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
D. $\left[\frac{-\pi}{4}, \frac{\pi}{4}\right]$

CBSE | Class 12 | Functions | Maths | RS Aggarwal

Mark (√) against the correct answer in the following: Let $f(x)=\cos ^{-1} 2 x$ . Then, $\operatorname{dom}(f)=?$
A. $[-1,1]$
B. $\left[\frac{-1}{2}, \frac{1}{2}\right]$
C. $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
D. $\left[\frac{-\pi}{4}, \frac{\pi}{4}\right]$

Solution:

Option(B) is correct.
$f(x)=\cos ^{-1}2 x$
Domain for function $\cos ^1 \mathrm{x}$ is $[-1,1]$ and range is $[0, \pi]$
When a function is multiplied by an integer, the domain of the function is decreased by the same number.
Therefore, domain of $\cos ^{-1} \mathrm{x}$ is $[-1,1]$
Multiplying the function by 2
$\Rightarrow$ domain of $\cos ^{-1}2 x$ is $\left[\frac{-1}{2}, \frac{1}{2}\right]$