Let $f \in L^1(\mathbb{R})$, $\lambda \in \mathbb{R}_+^*$ and let $g$ be the function from $\mathbb{R}$ to $\mathbb{C}$ such that $g(x) = f(\lambda x)$ for all real $x$. Show that $g \in L^1(\mathbb{R})$ and, for all real $\xi$, express $\hat{g}(\xi)$ in terms of $\hat{f}$, $\xi$ and $\lambda$.