Question

Let $f\left(x\right)$ be a real valued function, then the number of integral values of $x$ for which $f\left(x\right)=\sqrt{x+2}+\sqrt{7-x}$ is defined, is

Answer 1

$f\left(x\right)=\sqrt{x+2}+\sqrt{7-x}$
$f$ is meaningful if $x+2\ge 0$ and $7-x\ge 0$
$\Rightarrow x\ge -2$ and $x\le 7$
$\Rightarrow x\in [-2,7]$
Number of integral values in the interval $[-2,7]$ is $10$.