Let f: X rightarrow X be such that f(f(x)) = | vedclass

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(D) Given that $f(f(x)) = x$ for all $x \in X$. To check for one-to-one (injective): Let $f(x_1) = f(x_2)$. Applying $f$ on both sides, we get $f(f(x_

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$f$ is both one-to-one and onto

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(D) Given that $f(f(x)) = x$ for all $x \in X$. To check for one-to-one (injective): Let $f(x_1) = f(x_2)$. Applying $f$ on both sides, we get $f(f(x_1)) = f(f(x_2))$. Since $f(f(x)) = x$, this implies $x_1 = x_2$. Thus, $f$ is one-to-one. To check for onto (surjective): For any $y \in X$, let $x = f(y)$. Then $f(x) = f(f(y)) = y$. Since for every $y \in X$, there exists an $x \in X$ such that $f(x) = y$, $f$ is onto. Therefore, $f$ is both one-to-one and onto (bijective).

Let $f: X \rightarrow X$ be such that $f(f(x)) = x$ for all $x \in X$ and $X \subseteq \mathbb{R}$. Then:

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