Let f : [a, b] R be C1 on [a, b] with f(t) 0 for

Let f : [a, b] → R be C1 on [a, b] with fʹ(t) ≠ 0 for t ∈ [a, b]. Prove that the explicit curve x = f-1(y), as y runs from f(a) to f(b), is orientation equivalent to the explicit curve y = f(x), as x runs from a to b.