If F(w) is the Fourier transform of f(x), show that F(aw) is the Fourier transform of (1/a)f(x/a).
So if I apply a fourier transform to (1/a)f(x/a):
$$ \frac{1}{2\pi}\int_{-\infty}^\infty \frac{1}{a} f(\frac{x}{a}) e^{iwx} dx$$
i'm lost in how to get F(aw) from this
You may just perform the change of variable $u:=\dfrac x a$, $dx=adu$, to get $$ \frac{1}{2\pi}\int_{-\infty}^\infty \frac{1}{a}f(\frac{x}{a}) e^{iwx} dx= \frac{1}{2\pi}\int_{-\infty}^\infty f(u) e^{iawu} du=F(aw). $$