Question

what is the domain of the following rational function?
$f(x) = \frac{2x - 8}{x - 1}$
$circ$ ${x|x \
eq 2}$
$circ$ ${x|x \
eq 1}$
$circ$ ${x|x \
eq -1}$
$circ$ ${x|x \
eq 1}$

Explanation:

Step1: Identify denominator constraint

For a rational function, the denominator cannot equal 0. Set $x-1
eq 0$.

Step2: Solve for excluded x-value

Solve the inequality: $x
eq 1$.

Step3: Express domain in set notation

The domain is all real numbers where $x$ is not 1, written as $\{x|x
eq 1\}$.

Answer:

$\{x|x
eq 1\}$