Since a function is $f$, not $f(x)$, how do you denote $\int f(x,y)g(y)dy$?

Question

It's usually stated that the correct symbol of a function should be $f$, because $f(x)$ is the value of $f$ at the point $x$. I tend to follow this convention, but there are ocassions when this notation seem to be almost unsuitable.

For example, if there are several functions and variables:

$$\int _{-\infty}^\infty f(x,y)g(y)dy$$

Is there any nice way to denote the integral?

Answer 1

You could refer to the function $$ x \mapsto \int_{-\infty}^\infty f(x,y) g(y)\; dy$$