Answer
$f\circ g\circ h\ =\ \sqrt{\frac{5x+1}{4x+1}}$
Work Step by Step
$f(x)=\sqrt{x+1}$
$g(x)=\frac{1}{x+4}$
$h(x)=\frac{1}{x}$
$f\circ g\circ h=f(g(h(x)))$
First evalulate the composition of the inner two function as:
$g\circ h=g(h(x))$
$=\frac{1}{\frac{1}{x}+4}$
Smplify:
$=\frac{x}{1+4x}$
Now find the remaining part as:
$f\circ g\circ h=f(g(h(x)))$
$f(\frac{x}{1+4x})=\sqrt{\frac{x}{1+4x}+1}$
Simplify:
$=\sqrt{\frac{5x+1}{4x+1}}$
