Question

Suppose that the function r and a are defined for all real numbers x as follows R(x)=5x^3S(x)=x^2Write the expressions for (S.R) (x) and (S - R) (x) and evaluate (S + R) (2).

Answer 1

`\begin{gathered} (S\cdot R)(x)=5x^5 \\ (S-R)(x)=x^2-5x^3 \\ (S+R)(2)=44 \end{gathered}`

Explanation:

We have the following function:

`\begin{gathered} R\mleft(x\mright)=5x^3 \\ S\mleft(x\mright)=x^2 \end{gathered}`

We apply the expressions requested in each statement, just like this:

`\begin{gathered} \mleft(S\cdot R\mright)(x)=5x^3\cdot x^2=5x^5 \\ \mleft(S-R\mright)(x)=x^2-5x^3 \\ (S+R)(x)=x^2+5x^3 \\ (S+R)(2)=2^2+5\cdot2^3=4+5\cdot8=4+40=44 \end{gathered}`