Question

The domain of the function $f(x)=\sqrt{3-x}+{\cos }^{-1}\left(\frac{3-2x}{5}\right)$ , is

• A. $[-1,3]$
• B. $(-1,3]$
• C. $[-1,3)$
• D. None of these

Answer 1

Answer: (A)

We have, the function $f(x)=\sqrt{3-x}+{\cos }^{-1}\left(\frac{3-2x}{5}\right)$
For it's existence, $3-x\ge 0\Rightarrow x\le 3$ ... (i)
and $-1\le \frac{3-2x}{5}\le 1$
$\Rightarrow$ $-5\le 3-2x\le 5$
$\Rightarrow$ $-8\le -2x\le 2$
$\Rightarrow$ $-1\le x\le 4$ ... (ii)
From Eqs. (i) and (ii), it is clear that the domain of the given function $f$ is
$(-\infty ,3]\cap [-1,-4]=[-1,3]$