Question

hello i need help finding the domain of the function f(x)= 1/x^2-9

Answer 1

For:

$f(x)=\frac{1}{x^2-9}$

The domain of a function is the complete set of possible values of the independent variable. In this case, we can't divide by zero, since division by zero is undefined. Therefore:

$\begin{gathered} x^2-9\ne0 \\ x^2\ne9 \\ x\ne\sqrt[]{9} \\ x\ne\pm3 \end{gathered}$

Therefore, we can conclude the domain is:

$\begin{gathered} D\colon\mleft\lbrace x\in\R\colon x\ne-3_{\text{ }}and_{\text{ }}x\ne3\mright\rbrace \\ or \\ D\colon(-\infty,-3)\cup(-3,3)\cup(3,\infty) \end{gathered}$