Answer
a) $f(g(x))=\frac{6}{4+5x}$
b) $x\ne-5$, $x\ne-6/5$, $x\ne0$
Work Step by Step
$f(x)=\frac{x}{x+5}$ and $g(x)=\frac{6}{x}$
$x+5\ne0$ and $x\ne0$
$x\ne-5$ and $x\ne0$
a) $f(g(x))=\frac{\frac{6}{x}}{\frac{6}{x}+5}=\frac{6}{6+5x}$
b) $6+5x\ne0$
$x\ne-6/5$
Therefore, the domain of the composite function is all $R$ except $-5,-6/5,0$.
