The Fourier Integral

Let g∈S and define g a (x) = g(ax) for a > 0. Show that $${{\hat{g}}_{a}}(y) = \frac{1}{a}\hat{g}(\frac{y}{a})$$ In particular, if \(g(x) = {{e}^{{ - {{x}^{2}}}}}\),find \({{\hat{g}}_{a}}(x)\)