Prove that $f(A \backslash S) = B \backslash f(S)$
7127
Overview of basic results about images and preimages
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
60348
How do I prove $F(a)=F(a^2)?$
80199
Do we have always $f(A \cap B) = f(A) \cap f(B)$?
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
102553
How to show that $f(z) = f(i)$
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
14830
A transformation of F[x]
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
16092
How to prove that the composition of two surjective functions is surjective
127296
prove that a|b and b|a iff a=+-b
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
1770
Matrix $M_1 = M(f', \mathcal{B}, \mathcal{B '})$ of $f$