At the exam of Mathematics 3 I have to do an exercise about the Fourier Transform. For exemple, I have a certain $f(x)$, and i have to compute $$ \mathscr{F}[f(x)]= \hat{f}(\omega)= \int_{-\infty}^{\infty} f(x) e^{i\omega x}dx $$
My question is: is it possible, without calculating the anti-transform, to see if I have done some errors with the calculations? I mean, is it possible, looking the result,to understand intuitively if is it correct? In fact I don't have the time to anti-trasform $\hat{f}(\omega) $ to get the initial $f(x)$.