Question

Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer

Answer 1

The domain of a function is all values of x the function can have.

Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:

`\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}`

Since the first condition contains the second, so the domain set is represented by the second condition:

`(6,\text{inf)}`