Question

question 26, 2.6.41 part 7 of 8 given $f(x)=3 + \frac{8}{x}$ and $g(x)=\frac{8}{x}$ find $f + g,f - g,fg$, and $\frac{f}{g}$. determine the domain for each function. c. the domain of $f - g$ is $\varnothing$. $(fg)(x)=\frac{24x + 64}{x^{2}}$ (simplify your answer.) what is the domain of $fg$? select the correct choice below and, if necessary, fill in the answer - box to complete your choice. a. the domain of $fg$ is { } (use a comma to separate answers as needed.) b. the domain of $fg$ is $(-\infty,0)\cup(0,\infty)$. (type your answer in interval notation.) c. the domain of $fg$ is $\varnothing$. $(\frac{f}{g})(x)=\square$ (simplify your answer.)

Explanation:

Step1: Find domains of f and g

f(x)=3+8/x and g(x)=8/x are undefined at x=0. Domains: (-∞,0)∪(0,∞) for both.

Step2: Domain of fg is intersection

Product fg(x) is undefined where f or g is undefined (x=0). Thus, domain: (-∞,0)∪(0,∞).

Answer:

B. The domain of fg is (-∞,0)∪(0,∞)