Consider the the real number $k$ which satisfies $0 < k < 1$.
We are given two transformations $T_1(x) = kx$ and $T_2(x) = (1-k)x + k$.
Consider the set of real numbers over the interval $[0, 1]$. Now consider some smaller interval $[a, b] \in [0, 1]$. Given a starting point x = k, the goal is to show that through a sequence of the above transformations, a point can be reached that is in the interval $[a, b]$.