# Homework Help: Fourier Transform

1. Dec 3, 2005

### Chen

How can I prove that doing a Fourier transform on a function f(x) twice gives back f(-x)?

Thanks..

2. Dec 3, 2005

### Tide

I think you're asking about the double integral

$$\int_{-\infty}^{\infty} e^{i kx} dk \int_{-\infty}^{\infty}e^{ikx'} f(x')dx'$$

If so, then the outer integral

$$\int_{-\infty}^{\infty}e^{i k (x+x')} dk = \delta (x+x')$$

i.e. the Dirac delta function and you arrive at your result upon evaluating the inner integral. (That's ignoring factors of $2\pi$ which I am sure you can handle!)

Last edited: Dec 3, 2005
3. Dec 3, 2005

### Chen

I should hope so. Thanks!