Well, you know that F^-1 is an inverse function of an arbitrary function. Something you need to keep in mind is that F(F^-1(X)) is equal to X because the Function of the inverse function gives you the variable. As a result, what we did in this problem is first we wrote the P(X < x), and because X is an inverse function, we took the function of both sides. As a result, we got (U<= F(x))
I hope that helps
