Question

Suppose that the functions f and g are defined for all real numbers x as follows.5 (x) =3738 (x) =x?Write the expressions for (f+g) (x) and (f-g) (x) and evaluate (f-g)(-2).

Answer 1

Given:

`\begin{gathered} f(x)=3x^3 \\ g(x)=x^2 \end{gathered}`

Question 1:

`\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=3x^3+x^2 \end{gathered}`

Question 2:

`\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=3x^3\cdot x^2 \\ (f\cdot g)(x)=3x^5 \end{gathered}`

Question 3:

`\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=3x^3-x^2 \\ (f-g)(-2)=3(-2)^3-(-2)^2 \\ (f-g)(-2)=-24-4 \\ (f-g)(-2)=-28 \end{gathered}`