Question

Write the expressions for (s + r)(x) and (sr)(x) and evaluate (s - r)(- 1) .Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 4x ^ 2 s(x) = 2x

Answer 1

Solution

Given

$\begin{gathered} r(x)=4x^2 \\ s(x)=2x \end{gathered}$$\begin{gathered} (s+r)(x)=s(x)+r(x)=2x+4x^2 \\ \\ \Rightarrow(s+r)(x)=2x+4x^2 \end{gathered}$$\begin{gathered} (s\cdot r)(x)=s(r(x))=s(4x^2)=2(4x^2)=8x^2 \\ \\ \Rightarrow(s\cdot r)(x)=8x^2 \end{gathered}$

$\begin{gathered} (s-r)(-1)=s(-1)-r(-1)=2(-1)-4(-1)^2=-2-4=-6 \\ \\ (s-r)(-1)=-6 \end{gathered}$