Two functions f(x) and g(x) are inverses if and only if:
f( g(x)) = g(f(x)) = x.
With that, we will find that the correct option is: g(x) = 2*x - 16
Let's see how to find the inverse of the given function.
The given function is: f(x) = (1/2)*x + 8
Notice that this is linear, thus, we propose an inverse that is also linear:
g(x) = a*x + b
Now we evaluate g(x) in f(x) to get:
g(f(x)) = a*f(x) + b
And that must be equal to x, so we get:
a*f(x) + b = x
a*((1/2)*x + 8) + b = x
(a/2)*x + a*8 + b = x
Then we have two equations:
(a/2) = 1, so a = 2.
a*8 + b = 0
And we know that a = 2, so we can replace that:
2*8 + b = 0
b = -16
Then the inverse function is:
g(x) = 2*x - 16
If you want to learn more, you can read:
brainly.com/question/2541698
