Question

The domain of the function ${\cos }^{-1}(3x-2)$ is

• A. $\left(\frac{1}{3},1\right]$
• B. $\left(-1,\frac{1}{3}\right]$
• C. $\left(-1,1\right]$
• D. $\left(-\frac{1}{3},\frac{1}{3}\right]$

Answer 1

The correct option is A $\left(\frac{1}{3},1\right]$

$\mathrm{For}{\cos }^{-1}x,-1\le x\le 1.$
$\therefore \mathrm{For}{\cos }^{-1}\left(3x-2\right)-1\le \left(3x-2\right)\le 1$
$\Rightarrow 1\le 3x\le 3\Rightarrow \frac{1}{3}\le x\le 1.$