Solution:
Given:
The following functions;
[tex]\begin{gathered} f(x)=\frac{8}{x+4} \\ g(x)=\frac{6}{5x} \end{gathered}[/tex]
To find the indicated composition (fog)(x).
[tex]\begin{gathered} (\text{fog)(x) means } \\ f(g(x))\text{ means in the function f(x), replace x with g(x)} \end{gathered}[/tex][tex]\begin{gathered} f(x)=\frac{8}{x+4} \\ (\text{fog)(x)}=\frac{8}{\frac{6}{5x}+4} \\ (\text{fog)(x)}=\frac{8}{\frac{6+20x}{5x}} \\ (\text{fog)(x)}=8\times\frac{5x}{6+20x} \\ (\text{fog)(x)}=\frac{40x}{6+20x} \\ (\text{fog)(x)}=\frac{2(20x)}{2(3+10x)} \\ (\text{fog)(x)}=\frac{20x}{3+10x} \end{gathered}[/tex]
Therefore,
[tex](\text{fog)(x)}=\frac{20x}{3+10x}[/tex]
