A1 The function f(x) is defined by f(x) = { { 1 1- ½½|x| for |x| ≤ 2 for |x| >2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f'] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = sin² k k2 dk = π. 0, to show (1)

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