(a) Are the following expressions even or odd? Sums and products of even functions and of odd functions, products of even times odd functions. Absolute values of odd functions f(x) + f(– x) and f(x) – f(– x) for arbitrary f(x).
(b) Write ekx, 1/(1 – x), sin (x + k), cos h(x + k) as sums of an even and an odd function.
(c) Find all functions that are both even and odd.
(d) Is cos3 x even or odd? Sin3 x? Find the Fourier series of these functions. Do you recognize familiar identities?