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## Homework Statement

The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and inverse transform.

## Homework Equations

The Fourier and the Inverse Fourier transform integrals

## The Attempt at a Solution

Do I need to prove the inverse fourier theorem or is there a simpler solution?

One attempt that I have seen at recovering the original function using the inverse fourier transform formula integrates the exponent part to a sin(Mx)/x type function, which is then shown to approach the delta function as M approaches ∞.