Question

Let f:R+→[9,∞) given by f(x)=x^2+9. Find the inverse of f.

(a) \(\sqrt{x-9}\)

(b) \(\sqrt{9-x}\)

(c) \(\sqrt{x^2-9}\)

(d) x^2+9

This question was addressed to me during an interview.

This key question is from Composition of Functions and Invertible Function in section Relations and Functions of Mathematics – Class 12

Answer 1

Correct answer is (a) \(\sqrt{x-9}\)

For explanation: The function f(x)=x^2+9 is bijective.

Therefore, f(x)=x^2+9

i.e.y=x^2+9

x=\(\sqrt{y-9}\)

⇒f^-1 (x)=\(\sqrt{x-9}\).