Question

Suppose that the functions and s are defined for all real numbers x as follows r(x) = 4x; s(x) = 3x ^ 2 Write the expressions for (s + r)(x) and (sr)(x) and evaluate (s - r)(2) .

Answer 1

Given

`\begin{gathered} r(x)=4x \\ \\ s(x)=3x^2 \end{gathered}`

Then

`\begin{gathered} (s+r)(x)=s(x)+r(x)=4x+3x^2 \\ \\ \Rightarrow(s+r)(x)=4x+3x^2 \end{gathered}`
`(s\cdot r)(x)=s(r(x))=s(4x)=3(4x)^2=3*16x^2=48x^2`
`(s-r)(2)=s(2)-r(2)=3(2)^2-4(2)=12-8=4`