find the domain of the following rational function.\ng(x)=\\frac{-5x^{2}}{(x - 9)(x + 8)}

Explanation:

Step1: Recall the domain rule for rational functions

The domain of a rational function (y = \frac{f(x)}{g(x)}) is all real numbers (x) except those for which (g(x)=0).

Step2: Set the denominator equal to zero

Set ((x - 9)(x + 8)=0). Using the zero - product property (ab = 0) implies (a=0) or (b = 0). So (x-9=0) gives (x = 9), and (x + 8=0) gives (x=-8).

Answer:

The domain of (g(x)) is ({x|x\neq - 8,x\neq9,x\in R}) (or in interval notation ((-\infty,-8)\cup(-8,9)\cup(9,\infty)))