$L_2$ integrability of function composition

Question

Let $f:R^n \rightarrow R^n$ and $g:R^n\rightarrow R$. Suppose that $g$ is square integrable, i.e. $\int_{R^n}|g(x)|^2 dx < \infty$. Under what conditions on $f$ (if any) is it appropriate to say that $g\circ f$ is also square integrable? The measure here is the Lesbegue measure on $R^n$.