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The function f:R→R defined by f(x)=5x+9 is invertible.(a) True(b) FalseThis 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»

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.



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