determine the domain of each of the following

Question

Determine the domain of each of the following functions.

                        f( x ) = x - 4 / x² - 2 x -15

Solution

With this problem we have to avoid division by zero and thus we have to determine where the denominator is zero that means solving,

x² - 2 x -15 = ( x - 5) ( x + 3) =0

⇒  x = -3, x = 5

Thus, these are the only values of x that we have to avoid and therefore the domain is,

Domain: All real numbers except x = -3 & x = 5