Question

Can you help me solve it step by step. I dont understand it.

Answer 1

Given:

The following functions;

`\begin{gathered} f(x)=(8)/(x+4) \\ g(x)=(6)/(5x) \end{gathered}`

To find the indicated composition (fog)(x).

`\begin{gathered} (\text{fog)(x) means } \\ f(g(x))\text{ means in the function f(x), replace x with g(x)} \end{gathered}`
`\begin{gathered} f(x)=(8)/(x+4) \\ (\text{fog)(x)}=(8)/((6)/(5x)+4) \\ (\text{fog)(x)}=(8)/((6+20x)/(5x)) \\ (\text{fog)(x)}=8*(5x)/(6+20x) \\ (\text{fog)(x)}=(40x)/(6+20x) \\ (\text{fog)(x)}=(2(20x))/(2(3+10x)) \\ (\text{fog)(x)}=(20x)/(3+10x) \end{gathered}`

Therefore,

`(\text{fog)(x)}=(20x)/(3+10x)`