Question

The function f:R→R defined by f(x)=5x+9 is invertible.

(a) True

(b) False

This question was posed to me in an interview for internship.

This is a very interesting question from Composition of Functions and Invertible Function topic in chapter Relations and Functions of Mathematics – Class 12

Answer 1

Correct option is (a) True

Explanation: The given statement is true. A function is invertible if it is bijective.

For one – one: Consider f(x1)=f(x2)

∴ 5x1+9=5x2+9

⇒x1=x2. Hence, the function is one – one.

For onto: For any real number y in the co-domain R, there exists an element x=\(\frac{y-9}{5}\) such that f(x)=\(f(\frac{y-9}{5})=5(\frac{y-9}{5})\)+9=y.

Therefore, the function is onto.