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Let $f: X \rightarrow X$ be such that $f[f(x)]=x,$ for all
$x \in X$ and $X \subseteq R,$ then
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$x \in X$ and $X \subseteq R,$ then
Solution:
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Verified Answer
The correct answers are:
$f$ is one-to-one, $f$ is onto
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.
Now, $\quad f^{-1}(x)=f(x)$
Le. $f(x)$ is bijective.
Hence, $f(x)$ has to be one-one and onto.
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