Question

Given f (x) = 1/2x+8, which equation represents the inverse, g (x)?

Answer 1

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