LaTeX symbols - Function

Symbol Command
$f : A \to B$ f : A \to B
$f : A \rarr B$ f : A \rarr B
$f : A \rightarrow B$ f : A \rightarrow B
$f : A \rightarrow B$ f : A \rightarrow B
Symbol Command
$f : A \to B$ f : A \to B
$f \colon A \to B$ f \colon A \to B
Symbol Command
$A \overset{f}{\to} B$ A \overset{f}{\to} B
$A \overset{function}{\to} B$ A \overset{function}{\to} B
$A \xrightarrow{function} B$ A \xrightarrow{function} B
$A \xrightarrow[morphism]{function} B$ A \xrightarrow[morphism]{function} B
$A \xrightarrow{\text{function}} B$ A \xrightarrow{\text{function}} B
$A \xrightarrow[\text{morphism}]{\text{function}} B$ A \xrightarrow[\text{morphism}]{\text{function}} B
Symbol Command
$f : x \mapsto y$ f : x \mapsto y
$f \colon x \mapsto y$ f \colon x \mapsto y
Symbol Command
$x \overset{f}{\mapsto} y$ x \overset{f}{\mapsto} y
$x \overset{function}{\mapsto} y$ x \overset{function}{\mapsto} y
$x \xmapsto{function} y$ x \xmapsto{function} y
$x \xmapsto{\text{function}} y$ x \xmapsto{\text{function}} y
Symbol Command
$f(x)$ f(x)
$f(X)$ f(X)
$f[x]$ f[x]
$f[X]$ f[X]
$f(\cdot)$ f(\cdot)
Symbol Command
$f \vert A$ f \vert A
$f \vert{A}$ f \vert{A}
$f \vert_{A}$ f \vert_{A}
$f \mid_{A}$ f \mid_{A}

f |_{A} is incorrect and vert works well.

Symbol Command
$f \circ g$ f \circ g
$f \ast g$ f \ast g
Symbol Command
$f^{-1}$ f^{-1}
$\hat{f}$ \hat{f}

LaTeX function

LaTeX