Answer to Question #98485 in Algebra for Alexandra

Question

Consider the expression LaTeX: \frac{\sqrt{x-4}}{x-7} x − 4 x − 7 . What is the domain of the numerator? Explain how you know. What is the domain of the denominator? Explain how you know.

Put both parts together to define the domain for the entire expression. Enter your response in the submission window.

Answer 1

$\frac{\sqrt{x-4}}{x-7} x − 4 x − 7$

The domain of the numerator $\sqrt{x-4}$ is x-4≥0, that is, x ≥ 4.

The domain of the denominator {x-7} is x-7≠0, that is, x ≠ 7.

The domain of the whole expression is $x ≥ 4 \land x ≠ 7$.