How do I convert f(x) into its Fourier Transform?

[E&M]

Homework Statement

I am really confused in my electrodynamics class. I have the following function.

f(x) = \delta (x + \alpha ) + \delta(x -\alpha)

How do i convert this into Fourier Tranform ?
Those are dirac delta functions on either sides of the origin.

Homework Equations

no clue

The Attempt at a Solution

I multiplied f(x) by 1/sqrt(2*pi)*e-^ikt and integrated the whole thing.

 

[Donaldos]

And what did you get?

 

[E&M]

1/\sqrt{2\pi}\int\delta(x+\alpha)e^-ikx + \delta(x-\alpha)e^-ikx dx

I tried to integrate those terms by parts (uv substitution).

\int\delta(x+\alpha) = 1. Isn't that right ?
Also I think f(x)\int\delta(x+\alpha) = f(\alpha). Am i right ?

 

[Donaldos]

All you need is the following property:

\int\limits_{-\infty}^{+\infty} f(x)\delta\left(x-a\right)=f(a)

 

[E&M]

so

\inte^-ikx \delta (x - a) = e^-ika ?

 

[Donaldos]

Exactly.