Question

Consider f: R₊ → [−5, ∞) given by f(x) = 9x² + 6x − 5. Show that f is invertible with.

Answer 1

f: R₊ → [−5, ∞) is given as f(x) = 9x² + 6x − 5.

Let y be an arbitrary element of [−5, ∞).

Let y = 9x² + 6x − 5.

∴f is onto, thereby range f = [−5, ∞).

Let us define g: [−5, ∞) → R₊ as

We now have:

∴and

Hence, f is invertible and the inverse of f is given by