4. Let f : [0, 1] → (0, 1] be a continuous function such that f(0) = 0 and f(1) = 1. Consider the sequence of functions fn : [0,

1] → [0, 1] defined as follows: f_{1}=f \text { and } f_{n+1}=f \circ f_{n} \text { for } n \geq 1 \text { Prove that if }\left\{f_{n}\right\}_{n \geq 1} \text { converges uniformly, then } f(x)=x \text { for all } x \in[0,1] \text {. }