# Function Composition

## Homework Statement

If $$f$$ is some function defined at points "s" and "t," is there any way to simplify the following expression?

$$f((f(t)-f(s))$$

## Homework Equations

None that I know of.

## The Attempt at a Solution

I've been tinkering with this for a while and so far, I've determined the answer to be no. I know that

$$f(t)-f(s)\neq f(t-s)$$

in general, and that implies that

$$f(f(t)-f(s))\neq f(f(t))-f(f(s))$$

But does anyone know another way to simplify this to maybe some kind of composition?

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hunt_mat
Homework Helper
Let f(x)=sin x to give you a few ideas, I think the general answer is no.

$$sin(sin(t)-sin(s)) = [sin\circ sin(t)][cos\circ sin(s)] - [sin\circ sin(s)][cos\circ sin(t)]$$

Well that's a mess and a half. It is as I feared