How to find inverse Fourier transform I have the function
$$ \delta(f-2) $$
How can we inverse Fourier transform it? It's easy if $f$ is replaced with $w$. But based on my knowledge, $w = 2\pi f$.
The correct answer is 
$$ e^{4\pi i t} $$
Can somebody explain to me what happened? Thanks.

The inverse Fourier transform of $\delta(f-2)$ is
$$\mathcal F^{-1}[\delta](t) = \int \delta(f-2) e^{i2\pi ft} \, df = e^{i2\pi2t} = e^{i4\pi t}$$
The 2nd equality holds by definition of the delta function.
