Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

Let $f(x)=\cos ^{-1} 2 x .$ Then, 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:

$f(x)=\cos ^{-1} 2 x$

domain of $\cos ^{-1} x=[-1,1]$

on multiplying by an integer the domain decreases by same number

$\Rightarrow$ domain of $\cos ^{-1} 2 x=[-1 / 2,1 / 2]$

 

 

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