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 :)

Let $x$ be in $f^{-1}(f(A))$.
$x\in f^{-1}(f(A)) \implies$
$f(x) \in f(A) \implies$
$\exists a \in A : f(x)=f(a)$.
$f(x)=f(a)$ and $f$ injective $ \implies$
$x=a$
$x=a$ and $a\in A \implies x\in A$
each $x$ of $f^{-1}(f(A))$ is in $A$.
thus
$$f^{-1}(f(A)) \subset A$$
