Final answer:
Option B, f(x) = (x - 2)/5, is the correct answer as it is the inverse function of f(x) = 5x + 2, because when we substitute the function into itself, it returns the original variable x.
Step-by-step explanation:
To show that a function is the inverse function of another, we need to check if applying one function to the result of the other returns us to our original input. For the function f(x) = 5x + 2, we look for a function g(x) such that f(g(x)) = x and g(f(x)) = x. Let's test the given options:
- A. f(x) = 5x - 2 does not work because substituting it into the other function does not return x.
- B. f(x) = (x - 2)/5 works because if we substitute x with 5x + 2, we get ((5x + 2) - 2)/5 = x, showing it is the inverse.
- C. f(x) = 2x - 5 does not work because substituting it into the other function does not return x.
- D. f(x) = (x + 2)/5 does not work because substituting it into the other function does not return x.
Therefore, Option B is the correct answer, f(x) = (x - 2)/5, as it is the inverse function of f(x) = 5x + 2.