Answer
$(y+1) e^{x^{2} z^{2} (y+1)} =F(f(x), g(y), h(z))$
Work Step by Step
Given:
\[
y e^{x y z}=F(x, y, z)
\]
Also $f(x)=x^{2}, g(y)=y+1,$ and $h(z)=z^{2}$
We have to calculate $F(f(x), g(y), h(z)),$ substituting $x, y$ and $z$ in the function
\[
\begin{aligned}
& y e^{x y z}=F(x, y, z)= \\
g(y) e^{f(x) g(y) h(z)}=F(f(x), g(y), h(z)) & \\
(y+1) e^{x^{2} z^{2} (y+1)}=F(f(x), g(y), h(z)) &
\end{aligned}
\]
