Question

(f + g)(x)=\frac{3x + 16}{x} (simplify your answer.)
what is the domain of f + g? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the domain of f + g is (use a comma to separate answers as needed.)
b. the domain of f + g is (type your answer in interval notation.)
c. the domain of f + g is varnothing.

Explanation:

Step1: Identify denominator

Denominator of $(f+g)(x)=\frac{3x+16}{x}$ is $x$.

Step2: Find undefined point

Function undefined when $x=0$.

Step3: Determine domain

All real numbers except $0$; interval notation: $(-\infty,0)\cup(0,\infty)$.

Answer:

B. The domain of f + g is $(-\infty, 0) \cup (0, \infty)$ (Type your answer in interval notation.)