Answer:
[tex](r\circ q)(7)=8,\ (r\circ q)(7)=-8[/tex]
[tex](q\circ r)(7)=22[/tex]
Step-by-step explanation:
Composite Function
Given two functions q(x) and r(x), the composite function [tex]r\circ q(x)[/tex] is defined as
[tex](r\circ q)(x)=r(q(x))[/tex]
Similarily
[tex](q\circ r)(x)=q(r(x))[/tex]
The functions are
[tex]q(x)=x^2+6[/tex]
[tex]r(x)=\sqrt{x+9}[/tex]
Compute
[tex](r\circ q)(x)=\sqrt{x^2+6+9}=\sqrt{x^2+15}[/tex]
Evaluating for x=7
[tex](r\circ q)(7)=\sqrt{7^2+15}=\sqrt{64}=\pm 8[/tex]
We have two solutions
[tex]\boxed{(r\circ q)(7)=8,\ (r\circ q)(7)=-8}[/tex]
Now compute
[tex](q\circ r)(x)=(\sqrt{x+9})^2+6=x+9+6=x+15[/tex]
For x=7
[tex](q\circ r)(7)=7+15=22[/tex]
[tex]\boxed{(q\circ r)(7)=22}[/tex]
