Is it possible to convert the following function into specialized sub functions of individual variables?

Question

Is it possible to convert the following function

$$\sin(A-B)$$

into

$$f(g(A),B)?$$

where $g(x)$ is a function whose output ranges from 0 to 1 inclusive?

Answer 1

Any injection $g:\mathbb R\to[0,1]$ would do, since for any $g(x)$, we can compute $x$.

In other words, we define $f=\sin\;(g^{-1}(g(A))-B)$

For example, we can let $g(A)=\frac1\pi\tan^{-1}(A)+0.5$ (which has range $(0,1)$).

And $$f(g(A),B)=\sin(\tan(\pi(g(A)-0.5))-B)$$