The distinct linear function which maps [– 1, 1] onto [0, 2] is

Let the required function be f(x) = ax + bIf a > 0, then f(–1) = 0 and f(1) = 2⇒ –a + b = 0 and a + b = 2⇒ a = 1 and b = 1If a < 0, then f(–1) = 2 and f(1) = 0⇒ –a + b = 2 and a + b = 0⇒ a = –1 and b = 1Hence, f(x) = x + 1 or f(x) = –x + 1