hi alex,
you're probably bored of me by now, but i've been thinking again.
please could you see if this seems reasonable. i realise it's probably difficult to understand, without the graphs (sorry).

consider the set of axis "y" against "f(x)".

the line "y=f(x)" is a straight line through the origin.

the line "y=x" is the inverse of f(x). i.e. "y=(f^-1)(f(x))".

reflect this in the 'straight line' "y=f(x)" and you get
"y=f(f(x))", i think

this means that y=x reflected in y=f(x) gives y=ff(x)!

i realise that there's a problem with,for example f(x)=x^2 but i know that this comes from the squaring. it can be solved by reflecting y=mod(x)
im trying to do the same for y=g(x) reflected in y=f(x), but im not sure. at the moment i think its y=fg(-1)f(x).

sorry to bother you again, but thanx for your help. none of my tutors bother to help me.

thanx!