
Fourier transfrom proof
Under appropriate hypotheses on a function g = g(x) define on $\displaystyle \infty$ < x < $\displaystyle \infty$, show that
$\displaystyle \mathfrak{F}(g(xa))(\xi) = \hat{g}(\xi)e^{i{\xi}a}$
and
$\displaystyle \mathfrak{F}\left(\limits \int_{\infty}^{\infty}g(s)ds\right)(\xi) = \frac{\hat(g)(\xi)}{i\xi}$
I am confused with this question. It would seem that all I would have to do is do an inverse Fourier transform but that seems like it may be too easy. Any thoughts on how to start this?