If f(x) = x/(x - 1), find f(f)(x).
1. I don't like your notation, f is defined as a function on real numbers,
so what f(f)(x) means is debatable. I prefer the notation (f o f)(x) or f(f(x))
for composite function.
f(x)=x/(x-1),
so:
f(f(x))=f(x/(x-1)),
let y=x/(x-1), then:
f(f(x))=f(y)=y/(y-1)=[x/(x-1)]/[x/(x-1)-1]=[x/(x-1)]/[(x-(x-1))/(x-1)]=x
RonL