Question

Let f: N → N be a function defined as f(x) = 4x² + 12x + 15. Show that f : N → S is invertible (where S is range of f). Find the inverse of f and hence find f^-1(31) and f^-1 (87).

Answer 1

Let y be an arbitrary element of range f, then y = 4x² + 12x + 15 for some x in N, which implies that

y -15 = 4x² +12x

4(x² +3x) = y -15