I am issues with proving the following problem: $f^{-1}(f(A)) ⊃ A$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
60348
How do I prove $F(a)=F(a^2)?$
111515
Proving that $-a=(-1)\cdot a$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
157328
A complex analysis problem to prove an inequality
100399
A doubt with a part of a certain proof.
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$