Answer
$f(x)= \frac{1}{x}$
$g(x)=x+1$
$h(x)=x^{2}$
Other answers are also possible.
Work Step by Step
If we let:
$f(x)= \frac{1}{x}$
$g(x)=x+1$
$h(x)=x^{2}$
Then:
$(f\circ g\circ h)(x)=f(g(h(x))=\frac{1}{x^{2}+1}=F(x)$
Other answers are also possible.
