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**1. The problem statement, all variables and given/known data**

Let p:C[0,1]->C[0,1] the function that doing this "match":

For each f in C[0,1] , p(f)=f(x^2)

We need to prove that p is a continuous function.

**2. Relevant equations**

C[0,1] is the metric space of all the functions that are continuos in [0,1].

The distance between two functions g,f in C[0,1] is:

max{|f(t)-g(t)|} where t is in [0,1] ...

**3. The attempt at a solution**

I'm pretty sure we need to use the fact that if x is in [0,1] then x^2 is also in [0,1] ...

Maybe we should try using uniform continuity or Lifchitz Condition...

TNX to all the helpers!