Question

Let \(f: X \rightarrow X\) be such that \(f(f(x))=x\) for all \(x \in X\) and \(X \subseteq R\), then
(A) \(f\) is one-to-one
(B) \(f\) is onto
(C) \(f\) is one-to-one but not onto
(D) \(f\) is onto but not one-to-one

Answer 1

Ans : \((\mathrm{A}, \mathrm{B})\)
\(f(f(x))=x . \forall x \in X\)
so, \(f(x)=f^{-1}(x)\) i.e. \(f(x)\) is self invertible
Hence \(f(x)\) has to be one-one \& onto

Answer 2

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Answer 3

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