Final answer:
The value of (f^-1)(3) where f(2)=3 and f'(2)=6/7 is calculated using the inverse function formula to be 7/6.
Step-by-step explanation:
To find the value of (f-1)(3) using the given formula (f-1)(x) = 1 / f'(f-1(x)) and the provided information that f(2) = 3 and f'(2) = 6/7, we need to understand that we are essentially looking for the x-value for which the original function f yields the value 3, which we already know is 2. Since f maps 2 to 3, the inverse function f-1 will map 3 back to 2. We can then apply the formula, which simplifies in our case to (f-1)(3) = 1 / f'(2), since f-1(3) = 2. Knowing f'(2), we can compute (f-1)(3) = 1 / (6/7) or, after simplifying, 7/6.