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Function Composition

  • #1
129
0

Homework Statement



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

[tex]f((f(t)-f(s))[/tex]

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

[tex]f(t)-f(s)\neq f(t-s)[/tex]

in general, and that implies that

[tex]f(f(t)-f(s))\neq f(f(t))-f(f(s))[/tex]

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

Answers and Replies

  • #2
hunt_mat
Homework Helper
1,739
18
Let f(x)=sin x to give you a few ideas, I think the general answer is no.
 
  • #3
129
0
[tex]sin(sin(t)-sin(s)) = [sin\circ sin(t)][cos\circ sin(s)] - [sin\circ sin(s)][cos\circ sin(t)][/tex]

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

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