Equality using Parseval's theorem?

Question

Is it the following allowed using Parseval's theorem?

$$\int_{\infty}^{\infty} g(k) f(x)^2 dx = \frac{1}{2\pi}\int_{\infty}^{\infty} g(k) F(k)^2 dk$$

with $F(k)$ the Fourier transform of $f(x)$.