Determine the domain of extended-left-parenthesis Start Fraction f over g End Fraction extended-right-parenthesis left-parenthesis x right-parenthesis when lower f left-parenthesis x right-parenthesis equals negative Start Fraction 1 over x End Fraction and lower g left-parenthesis x right-parenthesis equals Start Root 3 x minus 9 End Root.
left-parenthesis 3 comma infinity right-parenthesis
Image with alt text: left-parenthesis 3 comma infinity right-parenthesis
left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 0 comma 3 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis
Image with alt text: left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 0 comma 3 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis
left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis
Image with alt text: left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis
left-parenthesis negative infinity comma 3 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis
The correct answer is:
left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 0 comma 3 right-parenthesis union left-parenthesis 3 comma infinity right-parenthesis