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Question 9

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

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:

∴ gof = IR+ and

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

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