Question

Find domain of the function $f\left(x\right)=\sqrt{4-\sqrt{5+2x}}$.

Answer 1

consider $f\left(x\right)=\sqrt{4-\sqrt{5+2x}}$

We must have

$4-\sqrt{5+2x}\ge 0$ and $5+2x\ge 0$

$\sqrt{5+2x}\le 4$ and $x\ge \frac{-5}{2}$

$5+2x\le 16$

$5x\le 11$

$x\le \frac{11}{2}$

Hence domain of $f\left(x\right)$ will be $[\frac{-5}{2},\frac{11}{2}]$