Q110 / 155 · WBJEE 2016 · Mathematics

Let $f: X \rightarrow X$ be such that $f[f(x)]=x,$ for all $x \in X$ and $X \subseteq R,$ then

  • Correct answer
    A
    $f$ is one-to-one
  • Correct answer
    B
    $f$ is onto
  • C
    $f$ is one-to-one but not onto
  • D
    $f$ is onto but not one-to-one

Solution

Given, $f(f(x)]=x$ Now, $\quad f^{-1}(x)=f(x)$ Le. $f(x)$ is bijective. Hence, $f(x)$ has to be one-one and onto.

Hence, the correct answer is options: 'A', 'B'.

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