Question

Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=x+1 s(x) = 4x +3 Write the expressions for (r*s)(x) and (r-s)(x) and evaluate (r+s) (4).

Answer 1

`\begin{gathered} r(x)=x+1 \\ s(x)=4x+3 \\ (r\cdot s)(x)=r(x)\cdot s(x)=(x+1)(4x+3)=4x^2+7x+3 \\ (r-s)(x)=r(x)-s(x)=x+1-(4x+3)=-3x-2 \\ (r+s)(x)=r(x)+s(x)=x+1+4x+3=5x+4 \\ (r+s)(4)=5(4)+4=24 \end{gathered}`