Problem 1. For functions f, g below, find a, b, c, d so that g(x) = a + b f(cx + d).
(a) f(x) = x, 0 <= x <= π, f is even and 2π-periodic; g(x) = 2x, 0 <= x <= 1/2; g(x) = 2 - 2x, 1/2 <= x <= 1, g is odd and is periodic with period 2.
(b) f(x) = 1, 0 <= x < π; f(x) = 0, π <= x < 2π, f is 2π-periodic; g(x) = 1, 0 <= x < 1/2; g(x) = -1, 1/2 <= x < 1, g is periodic with period 1.
(c) f(x) = x, -π <= x < π, f is 2π-periodic; g(x) = x, 0 <= x < 1, g has period 1.