Consider f :R^+ → [-5, ∞) given by f(x) = 9x^2 + 6x – 5. Show that fis invertible with f^-1(y) = √(y+6-1)/3

Question

Consider f :R⁺ → [-5, ∞) given by f(x) = 9x² + 6x – 5. Show that f is invertible with f^-1(y) = \(\frac{\sqrt{y + 6} - 1}{3}\)

Answer 1

f is invertible and f^-1 (y) = \(\frac{\sqrt{y + 6} + 1}{3}\)