Question

G(x) = x2 + 8x +12 over x² – 2x-8

a. For what value(s) of x is the function (x) undefined? Explain your reasoning and identify the domain
of the function G(x) in interval notation

Answer 1

The domain of the function in interval notation is -∞ < x < -2, -2 < x < 4, x > 4

Explanation:

The given function is presented as follows;

`G(x) = (x^2 + 8 \cdot x + 12)/(x^2 - 2 \cdot x - 8)`

The function given in rational format will not be defined when the value of the denominator = 0

Therefore, for the function to be undefined, we have;

x² - 2·x - 8 = 0

(x - 4)·(x + 2) = 0

Which gives;

x = 4, or x = -2

Therefore, the function is undefined for x = 4 and x = -2

The domain of the function in interval notation = -∞ < x < -2, -2 < x < 4, x > 4