Question

Consider f : R⁺ → [-9, ∞) given by f(x) = 5x² + 6x -9. Prove that f is invertible with f^-1(y) = (√ 54+5y-3/5) [where R⁺ is the set of all non-negative real numbers.

Answer 1

Here f : R⁺ → [-9, ∞) as

f(x) = 5x² + 6x - 9

First we shall show that f is one-one.