Answer
(f$\circ$g)(x)=$\frac{7}{\frac{2}{x}-4}$
The domain includes all real numbers except for 0, $\frac{1}{2}$, and 4.
Work Step by Step
Based on the denominators of the functions we know that for f(x) the domain does not include 4 and for g(x) the domain does not include 0. Both of these domain exclusions must also apply to (f$\circ$g)(x) as well.
(f$\circ$g)(x)=f(g(x))
(f$\circ$g)(x)=f($\frac{2}{x}$)
(f$\circ$g)(x)=$\frac{7}{\frac{2}{x}-4}$
$\frac{2}{x}$-4$\ne$0
$\frac{2}{x}$$\ne$4
4x$\ne$2
x$\ne$$\frac{1}{2}$
Therefore, the domain includes all real numbers except for $\frac{1}{2}$, 0, and 4.
