Final answer:
To find the derivative of the inverse function of f at the value a, we first need to find the inverse function. Then, we differentiate the inverse function and substitute the value a.
Step-by-step explanation:
The question asks us to find (f -1)'(a), which represents the derivative of the inverse function of f at the value a. To find this, we need to know the function f and its inverse function.
Let's say f(x) = y. To find the inverse function f -1, we interchange x and y and solve for y. Once we have the inverse function, we can differentiate it using the rules of differentiation to find (f -1)'(a).
For example, if f(x) = 2x + 3, then f -1(x) = (x - 3) / 2. To find (f -1)'(a), we differentiate f -1(x) with respect to x and substitute x = a in the resulting derivative.