Answer a and b

1. Even and Odd Functions. An even function is one such that f(x) = f(x). An odd function is one such that f(x) = f(x). (a) Show that for any function f on the domain [-T, ], (or any do- main symmetric about 0), is even, Seven (x) = f(x) + f +f(-x)) fodd (x)=(f(x) - f(x)) is odd, and f(x) = feven (x)+ fodd(). (b) Show the continuous Fourier transform of f is F(f) = = 1 2f(x)e-k dr feven (x) cos kx dx-i fodd(r) sin kr dr) 27Feven - 1 1 feven(x) cos kr dr-i -i fodd (r) sin kr dr)