Final answer:
The correct interpretation of the inverse of a function f, denoted as f(⁻¹)(a), for a given number a is option C: 1/f(a), which represents taking the reciprocal of the function value at a.
Step-by-step explanation:
The student is asking about how to find the inverse of a function, denoted as f(⁻¹)(a), and how it relates to a given number a. When we talk about the inverse of a function, we typically want to find a function that 'undoes' the effect of the original function f. The notation f(⁻¹)(a) is the value you get when you apply the inverse function of f to a.
From the given options, the correct interpretation of f(⁻¹)(a) is (C) 1/f(a). That's because the inverse function, in this case, can be thought of as taking the reciprocal of the function applied to a, which 'undoes' the multiplication effect of the original function f.