Question

=Knowledge CheckSuppose that the functions q and r are defined as follows.q(x)=x² +6r(x)=x+9Find the following.

Answer 1

(a) (r o q)(7) = 8

(b)

Explanation:

Given the functions:

`\begin{gathered} q(x)=x^2+6 \\ r(x)=\sqrt[]{x+9} \end{gathered}`

Part A

`(r\circ q)(7)=r\lbrack q(7)\rbrack`

First, evaluate q(7).

`q(7)=7^2+6=49+6=55`

Therefore:

`\begin{gathered} (r\circ q)(7)=r\lbrack q(7)\rbrack=r(55) \\ r(55)=\sqrt[]{55+9}=\sqrt[]{64}=8 \\ \implies(r\circ q)(7)=8 \end{gathered}`

Part B