Answer to Question #97890 in Algebra for ALexa

Question

Consider the expression
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.

Answer 1

The numerator is $x - 4$, hence its domain is $\mathbb{R}$. The denominator is $x - 7$, and it can not be equal to zero, hence the domain of the denominator is $x \in \mathbb{R} \setminus \{ 7\}$. The domain of the entire expression is the intersection of both, hence it is $x \in \mathbb{R} \setminus \{ 7\}$.