Is $(g \circ f)^{-1} (x)$ equal to $(f^{-1}\circ g^{-1})(x)$ or not?
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
40534
What is $(-1)^{\frac{2}{3}}$?
102777
Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
144439
For a $C^1$ function, the difference $|{g'(c)} - {{g(d)-g(c)} \over {d-c}} |$ is small when $|d-c|$ is small
108923
What is wrong with this false proof? $-1=(-1)^1=(-1)^\frac{2}{2}=((-1)^2)^\frac{1}{2}=\sqrt{(-1)^2}=\sqrt{1}=1$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
107390
Why is (-1)(-1) = 1?
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
11202
If $g \circ f$ is injective, so is $g$
58642
If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
80710
Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
101042
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
17310
Can $f(x)=|x|^3$ be differentiated
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$