# Origin of (f×g)(x) and (f∘g)(x) notations

Who and when began the writing of function multiplication, $$f(x)×g(x)$$, as $$(f×g)(x)$$ and of function composition, $$f\big(g(x)\big)$$, as $$(f∘g)(x)$$?

• I'm not sure it is possible to track down a person for this notation: Euler invented the notation $y=f(x)$ to denote the "function" relationship. But symbols like $\times$, $\cdot$, $*$ and $\circ$, $\bullet$ have been (and are still) used for all kinds of "multiplication like" operations, and it is only natural to jump from e.g. real numbers to functions whose codomain are real numbers. But I'd be curious to see if someone else has more success than I in tracking down a possible source:) Aug 17 '20 at 15:53
• I don't have an answer, but I guess that it started after 1900, since until then, the $f$ in $f(x)$ was not treated as a mathematical object per se. Aug 20 '20 at 9:02