Question

Suppose that the functions q and r are defined as follows. q (x) = x2 +4 r(x)=√x+5 Find the following. (gor) (4) = ? (roq) (4) = ?

Answer 1

$\begin{gathered} (q\circ r)(x)=(\sqrt[]{x+5})^2+4 \\ (q\circ r)(x)=x+5^{}+4\text{ (Raising to the power of 2)} \\ (q\circ r)(x)=x+9\text{ (Adding like terms)} \\ (q\circ r)(4)=4+9=13\text{ (Replacing 4 and Adding)} \\ \end{gathered}$

In the second case, we have:

$\begin{gathered} (r\circ q)(x)=\sqrt[]{(x^2+4)+5} \\ (r\circ q)(x)=\sqrt[]{x^2+9\text{ }}(\text{ Adding like terms)} \\ (r\circ q)(4)=\sqrt[]{(4)^2+9\text{ }}(\text{ Replacing x=4)} \\ (r\circ q)(4)=\sqrt[]{16^{}+9\text{ }}(\text{ Raising 4 to the power of 2)} \\ (r\circ q)(4)=\sqrt[]{25}\text{ (Adding)} \\ (r\circ q)(4)=5\text{ (Taking the square root)} \\ (r\circ q)(4)=5 \end{gathered}$