Answer
$ f(x)=x^{3}\qquad g(x)=x^{2}$
(sample answer)
Work Step by Step
Linear functions have the form $f(x)=mx+b$.
Let
$ f(x)=x^{3}\qquad$ (not linear)
$ g(x)=x^{2}\qquad$ (not linear)
$\displaystyle \frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{x^{3}}{x^{2}}=x$, which is linear (m=1,b=0)