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-7} }{\sqrt[]{x-4}} AnswerAnswer,AnswerAnswer

Answer 1

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

Since the values inside a square root need to be non-negative and the values in a denominator can't be zero, we can write the following restrictions:

`\begin{gathered} x-7\ge0 \\ x\ge7 \\ \\ x-4>0 \\ x>4 \end{gathered}`

The first condition is "inside" the second one, so we can use just the first one. Therefore, the domain is:

`\lbrack7,\text{inf)}`

The square bracket in the beginning represents that number 7 is also included in the domain.