Answer
a) $s=f(A)=\sqrt{\frac{A}{6}}$. The function $f$ gives the side of a cube in terms of its area $A$.
b) $
V=g(f(A))=s^3=\left(\sqrt{\frac{A}{6}}\right)^3
$
$V$ gives the volume, $V$, as a function of surface area, $A$,
Work Step by Step
(a) To write $s$ as a function of $A$, we solve $A=6 s^2$ for $s$
$$
s^2=\frac{A}{6} \quad \text { so } \quad s=f(A)= \sqrt{\frac{A}{6}}
$$
The function $f$ gives the side of a cube in terms of its area $A$.
(b) Substituting $s=f(A)=\sqrt{A / 6}$ in the formula $V=g(s)=s^3$ gives the volume, $V$, as a function of surface area, $A$,
$$
V=g(f(A))=s^3=\left(\sqrt{\frac{A}{6}}\right)^3
$$
