Prove or disprove $f^{-1}(A - B) = f^{-1}(A)-f^{-1}(B)$
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
86030
Prove or disprove - If a divides b and b divides a does a=b
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
127296
prove that a|b and b|a iff a=+-b
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
30860
Prove that $f(x)=0$ in $[-1,1]$.
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem