Needed help with math problem.

Question

C (x)= -4/x^2 - 16

What is the domain?

Answer 1

     C(x) = -4/x² - 16

The domain of the function C defined by an expression in terms of a variable x is the set of all real values of x which will allow the function to work. 

First let's combine the two terms in the function by finding a common denominator. The least common denominator among the two terms is x² so we will multiply the second term by x²/x²:

     C(x) = -4/x² - 16(x²/x²) = -4/x² - 16x²/x² = (-4 - 16x²)/x²

Notice that the function is undefined when the denominator is equal to 0. Thus, x² ≠ 0. This means, that all real numbers x will produce a valid output except when x² = 0 (i.e., the domain is all real numbers x except x=0). Therefore, the domain is as follows:

     set notation:   {all real numbers x ¦ x ≠ 0}

     interval notation:   (-∞, 0) and (0, ∞)