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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) .

Suppose that the functions and s are defined for all real numbers x as follows rx 4x sx 3x 2 Write the expressions for s rx and srx and evaluate s r2 class=

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Solution

Given

[tex]\begin{gathered} r(x)=4x \\ \\ s(x)=3x^2 \end{gathered}[/tex]

Then

[tex]\begin{gathered} (s+r)(x)=s(x)+r(x)=4x+3x^2 \\ \\ \Rightarrow(s+r)(x)=4x+3x^2 \end{gathered}[/tex][tex](s\cdot r)(x)=s(r(x))=s(4x)=3(4x)^2=3\times16x^2=48x^2[/tex][tex](s-r)(2)=s(2)-r(2)=3(2)^2-4(2)=12-8=4[/tex]

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