I'm reading the calculus test's answers and the professor wrote that representing the function. I wonder what the dot inside means.
"Given a function $F(x) = \frac{x^2+ 1}{x^2-1} \ , F$(•) doesn't touch the x axis in any point"
2 Answers
If $A$ and $B$ are sets we may define "single variable" functions between $A$ and $B$ as subsets of $A\times B$. Clearly this function is itself a set, but the elementary notation $f(x)$ to denote a function is also used for the evaluation of $f$ at $x$ (an element of $B$) rather than the function itself (a subset of $A\times B$). Merely saying $f:A\rightarrow B$ however leaves the number of arguments $f$ takes into doubt. $f(\cdot)$ is a way specifying there is a single argument while not confusing $f$ with some value in its range.
My complex analysis professor addressed this yesterday. He said
Normal people write it like this "f(x)".
Where the text in quotes appeared on the chalkboard.
