What is the Fourier transform of $f(-x)$? Can it be related to the Fourier transform of $f(x)$? Maybe, through odd/even properties?
Initially, I thought it is the same as the Fourier transform of $f(x)$. However, because of the scaling relation
$$\mathcal{F_{\omega}}f(-x) = \frac{1}{|-1|}\mathcal{F_{-\omega}}f(x)$$
Let: $$\hat{f}(t) = \int_{-\infty}^{\infty}f(x)e^{itx}dx.$$ You want to evaluate: $$\int_{-\infty}^{\infty}f(-x)e^{itx}dx $$ so you can make the change $u = -x$ so that: $$\int_{-\infty}^{\infty}f(-x)e^{itx}dx = -\int_{\infty}^{-\infty}f(u)e^{-itu}du = \int_{-\infty}^{\infty}f(u)e^{-itu}du$$ In other words, if $f(x) \to \hat{f}(t)$ then $f(-x) \to \hat{f}(-t)$.