Question So I know that the solution is but how exactly am

Question:

So, I know that the solution is , but how exactly am I finding the denominator part of the solution:? What does the inverse mean when applying to x value? How is the outcome 2?

Solution

that is just the definition of the derivitive of an inverse like this. f^-1(1) means find the x value that makes f(x)=1 so x=0 for this f. then find f\'(0)=2