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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