The domain of the real valued function $f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}}$ is
The domain of the real valued function $f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}}$ is
$[-1,2]$
$(-1,2)$
$[-1, \infty)$
$[2, \infty)$
Solution
Given, function is
$
\begin{aligned}
& f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}} \\
& x+3>0 \Rightarrow x>-3 ...(i)\\
& 2-x \geq 0 \Rightarrow x \leq 2 ...(ii)\\
& 1+x \geq 0 \Rightarrow x \geq-1...(iii)
\end{aligned}
$
From the above three inequalities, it can be concluded that $x \in[-1,2]$