# Show $f(x)=f_{0} + \int_{0}^{x} F \circ f$ has a unique solution.

I have an analysis exercise and I have literally no idea where to start or even a solid comprehension of what the question is. The exercise is as follows:

Now, if I am correct, $$\left| \Phi(f)(x)-\Phi(g)(x) \right|= d_{\mu}(\Phi(f),\Phi(g))$$, right? And it just means the distance between the two points.

I don't think it is needed but just in case, this is the referred to exercise 6.23: