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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

I have three questions:

(1) If $x\in R$, is it true that $f ^{-1} (f(x)) = x$?

(2) If $y\in R$, is it true that $f (f^{-1}(y)) = y$?

(3) If $B\subset R$, is it true that $f(f ^{-1} (B)$?

I think I have showed it for (3), but not sure of my proof. For (1) and (2), I considered the function $f (x) = x^2$. $f^{-1}(1)$ can be 1 and -1...

Thanks for the help!