Let I= [0, 1] be the unit interval. Suppose that f.g II are conjugate by a continuous map C: II. This means g(C(x)) = C(f(x)) for all x = I and C-: I I is also continuous. Show that if f has sensitive dependence on initial condition at x = I, then so does g at y = C(x) = I. (Hint: this problem is a bit tricky. Since C is continuous on a finite interval I, C- is uniformly continuous. This means for any do > 0, there exists another d> 0 such that for all yo, y I, if yoyd, then C(yo) - C-(91) < do. This implies (why?) that if |1 - ro> do, then C(x) C(ro) > d.)