prove $f^{-1}(C \cap D) = f^{-1}(C) \cap f^{-1}(D)$
110643
What are the strategies I can use to prove $f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$?
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
103854
Showing that $Q_n=D_n+D_{n-1}$
111515
Proving that $-a=(-1)\cdot a$
110826
prove that : $ i = \sqrt {-1}\ $
94383
Prove that $A^TD-C^TB=I$
145125
How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
107765
Prove that there exists two roots in $[-1,1]$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
132957
Prove that the derivative of $x^w$ is $w x^{w-1}$ for real $w$