Hello,

I've got to solve a following problem.

f is a function like this $\displaystyle f: X \rightarrow Y$. And two sets $\displaystyle A,B \subseteq X$. I've got to figure out how are the following two sets related:

$\displaystyle f^{-1}(f(A))$ and $\displaystyle A$

I got to here:

$\displaystyle x \in f^{-1}(f(A)) \Leftrightarrow f(x) \in f(A)$

Can I assume through this that $\displaystyle x \in A$? If so then how to correctly justify it?