Question:
Mark (√) against the correct answer in the following:.
Let $f(x)=\cos ^{-1}(3 x-1) .$ Then, dom $(f)=?$
A. $\left(0, \frac{2}{3}\right)$
B. $\left[0, \frac{2}{3}\right]$
C. $\left[\frac{-2}{3}, \frac{2}{3}\right]$
D. None of these
Solution:
$f(x)=\cos ^{-1}(3 x-1)$
domain of $\cos ^{-1} x=[-1,1]$
on multiplying by an integer the domain decreases by same number
$\Rightarrow$ domain of $\cos ^{-1} 3 x=[-1 / 3,1 / 3]$
$\Rightarrow$ domain of $\cos ^{-1}(3 x-1)=[1 / 3-1 / 3,1 / 3+1 / 3]=[0,2 / 3]$
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