Prove the convolution of f and g

[abstracted6]

This was the bonus question on my test, I couldn't really figure out how to begin.

 

[LCKurtz]

Start by writing the Fourier transform of$$
\int_{-\infty}^{\infty}f(x-y)g(y)dy$$
It will be an integral of that, so it will be a double integral. See if you can find a change of variables that allows you to separate the integrals.