when does $f(a)^{f(b)}=f(a^b)$?
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
66406
How to calculate $f(x)$ in $f(f(x)) = e^x$?
30685
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
38636
A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
3387
Derivative of $f(x)=|x|$
131844
When does $(e^a)^b = e^{ab}$ hold?
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
745
$F(x)$ versus $F[x]$ where $F$ is a field
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
108633
Why $f^{-1}(f(A)) \not= A$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
104394
What does $\int_{a}^{b} f(x)$ mean?
145424
If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
52461
Why does $(g^b \bmod m)^a \bmod m = (g^a \bmod m)^b \bmod m$?