Question

The domain of $f(x)={\cos }^{-1}(3x-1)$ is :

• A. $\left[0,\frac{2}{3}\right]$
• B. $\left[-\frac{2}{3},\frac{2}{3}\right]$
• C. $\left[0,-\frac{2}{3}\right]$
• D. none of these

Answer 1

Answer: (A)

Note: The domain of ${\cos }^{-1}x$ is
$-1\le x\le 1$
Then, the domain of ${\cos }^{-1}(3x-1)$ is
$-1\le 3x-1\le 1$
$\Rightarrow 0\le 3x\le 2\Rightarrow 0\le x\le \frac{2}{3}$
Then the domain of f(x) = $\left[0,\frac{2}{3}\right]$