Question

Help please thank you trying to learn before my upcoming test I have missed school due to health issues

Answer 1

Given:

`\begin{gathered} f(x)=(1)/(x-5) \\ g(x)=(3)/(x)+5 \end{gathered}`

To Determine:

`\begin{gathered} (fog)(x) \\ (gof)(x) \end{gathered}`

Solution

`\begin{gathered} (fog)(x)=f(g(x)) \\ (fog)(x)=f((3)/(x)+5) \\ (fog)(x)=(1)/((3)/(x)+5-5) \\ (fog)(x)=(1)/((3)/(x)) \\ (fog)(x)=1/(3)/(x) \\ (fog)(x)=1*(x)/(3) \\ (fog)(x)=(x)/(3) \end{gathered}`
`\begin{gathered} (gof)(x)=g(f(x) \\ (gof)(x)=g((1)/(x-5)) \\ (gof)(x)=(3)/((1)/(x-5))+5 \\ (gof)(x)=3/((1)/(x-5))+5 \\ (gof)(x)=3*(x-5)+5 \\ (gof)(x)=3x-15+5 \\ (gof)(x)=3x-10 \end{gathered}`

Hence,

`\begin{gathered} (fog)(x)=(x)/(3) \\ (gof)(x)=3x-10 \end{gathered}`