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Questions › DSE › DSE 2021 › Q2
4 marks, −1Mathematics › Sets, relations and functions › One-to-one, onto and invertible functionsHardabout 2 min

DSE 2021 Question 2: Sets, relations and functions

Let fff be a real-valued, continuous function defined on the set of all real numbers, satisfying f(f(x))=xf(f(x)) = xf(f(x))=x for all x∈Rx \in \mathbb{R}x∈R. If fff is not the identity function, then which of the following is true?

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Let f be a real-valued, continuous function defined on the set of all real numbers, satisfying f(f(x)) = x for all x ∈ ℝ. If f is not the identity function, then which of the following is true? (A) f is a constant function (B) f is a strictly decreasing function (C) f is a strictly increasing function (D) No function other than the identity function can satisfy this property

Also written as: Let f be a real-valued, continuous function defined on the set of all real numbers, satisfying f(f(x)) = x for all x in R. If f is not the identity function, then which of the following is true?

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on One-to-one, onto and invertible functions, part of Sets, relations and functions in Mathematics.

Injective, surjective and bijective functions and when an inverse exists.

TestStop has 11 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q13Let f:[0,∞)→ℝ be defined by f(x) = (x+1)/(x+2) for all x in the domain. Then f is
Practise Sets, relations and functionsMore on One-to-one, onto and invertible functions

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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.