Are the Fourier transforms of a function and its inverse related?

[john1989]

Hi

Does anyone know if there is a relation between the Fourier transform of a function and the Fourier transform of the inverse function

in summary
FT[f(x)] ?= FT[f^-1(x)]

Thanks!

 

[Vargo]

Logically they must be related because a 1-1 function uniquely determines its own inverse. Therefore, the Fourier transforms are at least related through this indirect relationship. However, I don't think there is any reasonable formula to relate the two. The Fourier transform does not interact with composition of functions in a simple way.