[Axiom-math] lot of questions about functions.

[Francois Maltey]

Hello, 

Is there a the difference between f := t -> 2*t + 1 and f(x)==2*x+1 ?

How can I do f o f o f o ...o f = x -> f(f(f(f...f(x)))) ?
   (I iterate 10 or 100 times)

f := x +-> 3*x 
g := x +-> 2*x+3  

It seems impossible to add 2 anonymous functions. 
I can compute f(x)+g(x) but I can't use (f+g)(x)

Can I do (f o g) or can I only compute f(g(x)) = f g x. 

With mupad (sqrt@@2)(16) and (address@hidden@sin)(PI) compute $2$ and $0$.