Question

The domain of $f\left(x\right)=co{s}^{-1}\left(\sqrt{3x}\right)$ is

• A. $[-1,1]$
• B. $[0,\frac{1}{3}]$
• C. $[0,1]$
• D. $[0,3]$

Answer 1

Answer: (B)

$[0,\frac{1}{3}]$

For $f$ to be defined $\sqrt{3x}$ has to exist.
$\Rightarrow 3x\ge 0$
$x\ge 0$
${\cos }^{-1}$ is defined only if $-1\le \sqrt{3x}\le 1$
As $x\ge 0$
$\Rightarrow \sqrt{3x}\le 1$
$\Rightarrow x\le \frac{1}{3}$
$\therefore x\in [0,\frac{1}{3}]$