Alternative notations for the function $f(a+b)$ to avoid confusion with $fa+fb$

Question

What are some good alternatives to avoid mix-up with $f(x)$ where f is a function and $f(x)$ where f is a constant? I was thinking of some additional symbols to the f-symbol, $f_{x}(x)$, or maybe using different brackets $f[x]$, but I'm mostly hoping that there were already some professionally used alternatives to imitate.

Thanks in advance

Answer 1

I know how you feel; I used to worry about this all of the time. The key thing to remember, however, is that the meaning should be clear from context.

I believe Mathematica uses brackets for functions, though, if you're set on changing notations.

Answer 2

The standard notation for continuous linear functional is $$\langle f, x\rangle_{X'\times X}$$

I guess we can do something like $$\langle f, x\rangle_{C(\mathbb{\mathbb{R}}) \times \mathbb{R}}$$ for continuous functions.

Answer 3

Normally scalars get put before vectors and functions to avoid this ambiguity - I would always assume $(a+b)f$ to be $af + bf$ and $f(a+b)$ to be $f$ evaluated at $a+b$.

If you're worried you could use $f[x]$, or always put $(a+b) \cdot f$ or something. I think the best thing really is to just follow the known conventions and be consistent (so if something is ambiguous, the reader has a context to put it into and figure it out).