Question

Consider f : [3, ∞) → [1, ∞) given by f(x) = x² – 6x + 10. Find f^-1

Answer 1

f(x) = (x – 3)² + 1

y = (x – 3)² + 1

⇒ (x – 3)² = y – 1

 ⇒ x = \(\sqrt{y-1} + 3\)

∴ f^-1(x) = \(\sqrt{x-1} + 3\)