Question

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

Answer 1

For:

`f(x)=(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\\e0 \\ x^2\\e9 \\ x\\e\sqrt[]{9} \\ x\\e\pm3 \end{gathered}`

Therefore, we can conclude the domain is:

`\begin{gathered} D\colon\mleft\lbrace x\in\R\colon x\\e-3_{\text{ }}and_{\text{ }}x\\e3\mright\rbrace \\ or \\ D\colon(-\infty,-3)\cup(-3,3)\cup(3,\infty) \end{gathered}`