QuestionFind the domain of $x$ for the expression $\frac{4}{x-19}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{4}{x-19}$ and asked to find the domain of $x$ . . The domain of a function or expression is the set of all possible values of the variable that will make the function or expression defined.
3. In this case, the expression is undefined when the denominator is zero, as division by zero is undefined in mathematics.

STEP 2

To find the domain, we need to find the values of $x$ that make the denominator zero, because these are the values that we need to exclude from the domain.
So, we set the denominator equal to zero and solve for $x$ $x-19 =0$

STEP 3

Rearrange the equation to solve for $x$ $x =19$

STEP 4

The value $x =19$ makes the denominator zero, so we must exclude this value from the domain.Therefore, the domain of the expression is all real numbers except $19$ .
In interval notation, this can be written as $(-\infty,19) \cup (19, \infty)$ .

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