Given the following functions f(x) and g(x), solve f over g(−3) and select the correct answer below:

f(x) = 6x + 8

g(x) = x − 2

−2
−negative one half
one half
2

We are given the functions:

f(x) = 6x + 8                        ---> 1

g(x) = x – 2                          ---> 2

To solve for the value of f over g(-3) or (f / g) (-3), we must first find (f / g) (x). We can do this by dividing equation 1 by equation 2:

(f / g) (x) = f (x) / g (x)

(f / g) (x) = (6 x + 8) / (x – 2)

Now we plug into the equation the value of x, x = - 3

(f / g) (- 3) = (6 * (-3) + 8) / (- 3 – 2)

(f / g) (- 3) = (- 18 + 8) / (- 5)

(f / g) (- 3) = - 10 / - 5

(f / g) (- 3) = 2

2