Is $g \circ f$ invertible if both $f$ and $g$ are invertible?
101042
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
134703
Let $X$ be a connected space, $f:X\to X$ continuous involution, $g:X\to\mathbb{R}$ continuous. Prove that $\exists$ $x\in X$ such that $g(x)=g(f(x))$.
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
55232
Show that $g\circ f\equiv 0$ implies $\det Df\equiv 0$, where $g(x_1,...,x_n)=x_1^5+...+x_n^5$
68724
$||T-I|| < 1$ implies that $T$ is invertible.
41363
when is f@g not the same as f[g]?
120960
$f,g$ such that $\int fg = \int f \int g$
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
63836
Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
76674
Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?