What is the Fourier Transform of f(-x)?

AI Thread Summary
The discussion centers on finding the Fourier transform of the function f(-x). It highlights that f(-x) can be classified as either even or odd, impacting its Fourier series representation. The user expresses confusion regarding the application of the Fourier transform, particularly the integral form involving complex exponentials. A general equation for the Fourier transform is mentioned, but the user seeks clarification on how to proceed with the calculation. The conversation emphasizes the need for a deeper understanding of the properties of even and odd functions in relation to Fourier transforms.
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Homework Statement


Find the Fourier transform of f(-x)


Homework Equations





The Attempt at a Solution


The way I tried to solve is
Fourier series is a sum of even and odd functions.
If f(-x) is even then, f(-x)=f(x)
If f(-x) is odd then, f(-x)= -f(x)

Sum of even and odd function is neither even nor odd.
I am lost after this. Any help?
 
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Can you write the general equation for finding a Fourier transform? Saying it is the "sum of even and odd functions" is pretty general. I've usually seen the transform as an integral containing a complex exponential or sines and cosines.
 
ok.
F(f(-x)) = int( f(-x) e^-i2pift dt)
Not sure how to solve this.
 

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