Let's define a function fff: f(x)=ax+bf(x) = ax + bf(x)=ax+b

We know, f2(x)=f(f(x))f^2(x) = f(f(x))f2(x)=f(f(x)) and f3(x)=f(f(f(x)))f^3(x) = f(f(f(x)))f3(x)=f(f(f(x))). We can write a generalized form, fn(x)=f(fn−1(x))f^n(x) = f(f^{n-1}(x))fn(x)=f(fn−1(x)), where n>1n > 1n>1.

This is a companion discussion topic for the original entry at https://toph.co/p/fun-with-functions