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I have to prove that if f [tex]\in[/tex] M(R) is odd/even, then [tex]\hat{f}[/tex] is odd/even

(where M(R) is the set of moderately decreasing functions)

I have used the rules that if f is even: f(x)=f(-x)

and if f is odd: -f(x)=f(-x)

and I have tried to link this with the definition of [tex]\hat{f}[/tex] but I am not getting the conclusion that I want, can anyone help? Thank you!