If f is injective can you prove this relation? Given that f maps E to F and A is a subset of E,  prove that if f is injective then f^-1(f(A)) is a subset of A.
Actually, im good at performing similar proofs, but i didn't understand why should f be injective? I proved it without using this given and didn't know how to benefit from it.
Please help me cz i have an exam.
Thanks :)

Choose $x\in f^{-1}(f(A))$. Then $f(x)\in f(A)$. Hence there exists $a\in A$ such that $f(x)=f(a)$. Injectivity of $f$ then implies that $x=a$. In particular, $x\in A$. Hence, $f^{-1}(f(A))\subset A$.
To show that injectivity is really needed, consider for instance the non-injective function
$$f:\{a,b,c\}\rightarrow\{a,b,c\}: \begin{cases} a\mapsto a\newline b\mapsto a\newline c\mapsto a \end{cases}.$$
If we take $A=\{a\}$, then $f^{-1}(f(A))=f^{-1}(\{a\})=\{a,b,c\}$ which is not a subset of $A$.
