Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q2

Answer 1

Given

`\begin{gathered} f(x)=7+(2)/(x) \\ g(x)=(2)/(x) \end{gathered}`

Then,

a)

`\begin{gathered} (f+g)(x)=f(x)+g(x)=7+(2)/(x)+(2)/(x)=7+(4)/(x) \\ \Rightarrow(f+g)(x)=7+(4)/(x) \end{gathered}`

b)

`\begin{gathered} (f-g)(x)=(7+(2)/(x))-(2)/(x)=7 \\ \Rightarrow(f-g)(x)=7 \end{gathered}`

c)

`\begin{gathered} (f\cdot g)(x)=(7+(2)/(x))\cdot((2)/(x))=(14)/(x)+(4)/(x^2) \\ \Rightarrow(f\cdot g)(x)=(14)/(x)+(4)/(x^2) \end{gathered}`

d)

`\begin{gathered} ((f)/(g))(x)=(f(x))/(g(x))=((7+(2)/(x)))/((2)/(x))=((7x+2)/(x))/((2)/(x))=(7x+2)/(2) \\ \Rightarrow((f)/(g))(x)=(7x)/(2)+1 \end{gathered}`