State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms of the following functions: - x| : (i) f(x) = { 1¹7 0 (ii) ƒ(x) = xe¯x²/4 x ≤ 1 : |xc|>1

Suppose a function f(x) = x between 0 and 1, and f(x) = 0 elsewhere. Solve for the fourier transform g(k) of the original function f(x).

2. Find the derivative of each funct Whenever possible, expand the log make use of the algebraic proper y = In(rVx² – 1) [49] a.