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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"

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2 Answers

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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.

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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.

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