Answer
$f(x)=\sqrt[3]{x}$
$g(x)=x-1$
$h(x)=\sqrt{x}$
Other answers are also possible.
Work Step by Step
If we let:
$f(x)=\sqrt[3]{x}$
$g(x)=x-1$
$h(x)=\sqrt{x}$
Then:
$(f\circ g\circ h)(x)=f(g(h(x))=\sqrt[3]{\sqrt{x}-1}=F(x)$
Other answers are also possible.