Question

Given that f(x)=x'2−12x and g(x)=x+12, find(a) (f+g)(x)=(b) (f−g)(x)=c) (fg)(x)= (d) (f/g)(x)=

Answer 1

Given:

`\begin{gathered} f(x)=x^2-12x \\ g(x)=x+12 \end{gathered}`

Required:

To find

`\begin{gathered} (f+g)(x) \\ (f-g)(x) \\ (fg)(x) \\ ((f)/(g))(x) \end{gathered}`

Step-by-step explanation:

Now

`\begin{gathered} (f+g)(x)=f(x)+g(x) \\ =x^2-12x+x+12 \\ =x^2-11x+12 \end{gathered}`
`\begin{gathered} (f-g)(x)=f(x)-g(x) \\ =x^2-12x-x-12 \\ =x^2-13x-12 \end{gathered}`
`\begin{gathered} (fg)(x)=f(x)g(x) \\ =(x^2-12x)(x+12) \\ =x^3+12x^2-12x^2-144x \\ =x^3-144x \end{gathered}`
`\begin{gathered} ((f)/(g))(x)=(f(x))/(g(x)) \\ \\ =(x^2-12x)/(x+12) \end{gathered}`

Final Answeer:

`\begin{gathered} (f+g)(x)=x^2-11x+12 \\ (f-g)(x)=x^2-13x-12 \\ (fg)(x)=x^3-144x \\ ((f)/(g))(x)=(x^2-12x)/(x+12) \end{gathered}`