Answer
a) $f(g(x))=\frac{4}{4+x}$
b) $x\ne-4$, $x\ne-1$, $x\ne0$
Work Step by Step
$f(x)=\frac{x}{x+1}$ and $g(x)=\frac{4}{x}$
$x+1\ne0$ and $x\ne0$
$x\ne-1$ and $x\ne0$
a) $f(g(x))=\frac{\frac{4}{x}}{\frac{4}{x}+1}=\frac{4}{4+x}$
b) $4+x\ne0$
$x\ne-4$
Therefore, the domain of the composite function is all $R$ except $-4,-1,0$
