Answer
a. $\frac{5x}{4x+1}$
b. $(-\infty,-\frac{1}{4})\cup(-\frac{1}{4},0)\cup(0,\infty)$
Work Step by Step
Given $f(x)=\frac{5}{x+4}, x\ne-4$ and $g(x)=\frac{1}{x}, x\ne0$, we have:
a. $(f\circ g)(x)=\frac{5}{1/x+4}=\frac{5x}{4x+1}$
b. The domain of the above function can be found as $\{x|x\ne-\frac{1}{4},0\}$ or $(-\infty,-\frac{1}{4})\cup(-\frac{1}{4},0)\cup(0,\infty)$ (note that $x=-4$ is in the domain)
