Why $f^{-1}(f(A)) \not= A$ Let $A$ be a subset of the domain of a function $f$.
Why $f^{-1}(f(A)) \not= A$.
I was not able to find a function $f$ which satisfies the above equation.
Can you give an example or hint.
I was asking for an example function which is not addressed 
here

If $f:X\longrightarrow Y$ is not injective and $A\subset X$. Then take $x \in X-A$ such that $f(x)=f(a)$ for some $a\in A$ then we have that $x\in f^{-1}(f(A))$ although $x\not \in A$. 
