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) = $\left[ 0 , \frac{2}{3} \right]$