Question

find the domain of the rational function. f(x) = 8/(x + 5) the domain is . (simplify your answer. type your answer in interval notation.)

Explanation:

Step1: Identify non - zero denominator condition

For a rational function $\frac{a}{b}$, $b
eq0$. Here $b = x + 5$, so $x+5
eq0$.

Step2: Solve the inequality

Solve $x+5
eq0$ for $x$. We get $x
eq - 5$.

Step3: Write in interval notation

The domain in interval notation is $(-\infty,-5)\cup(-5,\infty)$.

Answer:

$(-\infty,-5)\cup(-5,\infty)$