Fourier Transform of e^(ip0x)F(x) to F(p)

1. The problem statement, all variables and given/known data

f(p) is the Fourier transform of f(x). Show that the Fourier Transform of e^ip_ox f(x) is f(p- p₀).





2. Relevant equations

I'm using these versions of the fourier transform:

f(x)=1/√(2π)∫e^ixpf(p)dx

f(p)=1/√(2π)∫e^-ixpf(x)dx



3. The attempt at a solution



I have:

f(p)=1/√(2π)∫e^ix(p_o-p)f(x)dx

which is the same as:

f(p)=1/√(2π)∫e^-ix(p-p_o)f(x)dx

but I don't know where to go from here. I think I need to make a substitution using the original transform as I don't need to solve the integral. My other idea is that I have nearly proved it so just need to state the theory as to why this proves it; however, I don't know what that theory would be.

Any help would be appreciated!