This is a small part of a larger problem I am trying to solve. This is stated as a basic property of the fourier transform. First we define for $f \in L^1(\mathbb{R}^d)$ and $\lambda \neq 0$, $ \hat f(x) := \int_{\mathbb{R}^d} f(t) e^{-2\pi i t x} dt \quad\text{and}\quad \hat f_\lambda(x) := \lambda f(\lambda x). $
The property is that, $\hat f_\lambda(x) = \hat f(x/\lambda)$
I don't see how to prove this, not sure where to start really.
EDIT: The property I am trying to prove is the scaling property of this wikipedia article. http://en.wikipedia.org/wiki/Fourier_transform#Basic_properties