Question

Suppose that the functions and s are defined for all real numbers x as follows. r(x) = 3x ^ 3; s(x) = x ^ 2 Write the expressions for (s*varphi)(x) and (s + r)(x) and evaluate (s - r)(- 2) .

Answer 1

`\begin{gathered} r(x)=3x^3 \\ s(x)=x^2 \\ (s.r)(x)=3x^3* x^2 \\ =3x^5 \end{gathered}`
`(s+r)(x)=3x^3+x^2`
`\begin{gathered} (s-r)(x)=x^2-3x^3 \\ (s-r)(-2)=(-2)^2-3(-2)^3 \\ =4-3(-8) \\ =4+24 \\ =28 \end{gathered}`