Final answer:
To determine if two functions are inverses of each other, we need to check if their compositions equal the identity function. Option D, with f(x) = 2x^3-11 and g(x) = x + 11, is the correct pair of inverse functions.
Step-by-step explanation:
An inverse function undoes the operation of the original function, resulting in the input and output values switching places. To determine if two functions are inverses of each other, we need to check if their compositions equal the identity function, which is f(x) = x.
In Option A, f(x) = -14 and g(x) = 8x - 14. The compositions are:
f(g(x)) = f(8x - 14) = -14 and g(f(x)) = g(-14) = 8(-14) - 14 = -126.
Since f(g(x)) does not equal x and g(f(x)) does not equal x, Option A does not contain a pair of inverse functions.
Follow the same process for Options B, C, and D to determine the correct pair of inverse functions.
In Option B, f(x) = 3x^2 and g(x) = 3/(x+6). The compositions are f(g(x)) = f(3/(x+6)) = 3(3/(x+6))^2 and g(f(x)) = g(3x^2) = 3/(3x^2+6).
Continuing this process for all options, we find that the correct pair of inverse functions is Option D, where f(x) = 2x^3-11 and g(x) = x + 11.