Answer
f(g(x))=$\frac{5}{\frac{1}{x}+4}$
D=(-$\infty$,-4) U (-4,-$\frac{1}{4}$) U (-$\frac{1}{4}$,0) U (0,$\infty$)
Work Step by Step
f(g(x))=$\frac{5}{\frac{1}{x}+4}$
$\frac{1}{x}$+4$\ne$0
$\frac{1}{x}$$\ne$-4
x$\ne$-$\frac{1}{4}$
x+4$\ne$
x$\ne$-4
x$\ne$0
Therefore, the domain of the composite function includes all real numbers except -4, -$\frac{1}{4}$, and 0.