Question

Let f : N → R be a function defined as f(x) = 4x² + 12x + 15.

Show that f : N → S is invertible, where S is the range of f. Hence, find inverse of f.

Answer 1

Let y ∈ S, then y = 4x² + 12x + 15, for some x ∈ N.

Hence, fog (y) = I_S and gof (x) = I_N 

f is invertible, f^-1 = g