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