Composition of Functions

Example:

If $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=3x-5$ , then find $f\left(g\left(4\right)\right)$ .

Substituting $4$ for $x$ in the definition of the function $g$ , $g\left(4\right)=3\left(4\right)-5=7$ . Then, $f\left(g\left(4\right)\right)=f\left(7\right)$

$f\left(7\right)=\sqrt{7}$