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

Answer:

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 = I_R+and

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

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

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

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