Final answer:
The question requires the verification of the existence of an inverse function and finding its derivative at a certain point, but it cannot be completed as the original function f is not provided.
Step-by-step explanation:
The question seems to involve verifying that a function has an inverse and then finding the derivative of the inverse function evaluated at a specific point. To verify that a function f has an inverse, we need to show that the function is one-to-one (bijective). A function is one-to-one if no two different inputs produce the same output. After establishing that an inverse exists, we can use the formula for the derivative of the inverse function, which states that (f-1)'(a) = 1 / f'(f-1(a)), where a is the given real number, and f' represents the derivative of the original function f. However, as the function f itself is not provided in the question, we cannot proceed to calculate (f-1)'(a). The question needs to be revised or more information must be provided to find the derivative of the inverse function.