Show that if $f$ is injective, then $f^{-1}(f(C))=C$
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
72251
$g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
16092
How to prove that the composition of two surjective functions is surjective
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
115636
Show that $f$ is either injective or a constant function.
78698
Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
89514
Show that if $g \circ f$ is injective, then so is $f$.
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
50012
$f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
68746
What is $f(f^{-1}(A))$?