Question

Suppose that the functions q and r are defined as follows. q (x) = x^2+6 r(x) = square x+9

Answer 1

Answer:

$(r\circ q)(7)=8,\ (r\circ q)(7)=-8$

$(q\circ r)(7)=22$

Step-by-step explanation:

Composite Function

Given two functions q(x) and r(x), the composite function $r\circ q(x)$ is defined as

$(r\circ q)(x)=r(q(x))$

Similarily

$(q\circ r)(x)=q(r(x))$

The functions are

$q(x)=x^2+6$

$r(x)=\sqrt{x+9}$

Compute

$(r\circ q)(x)=\sqrt{x^2+6+9}=\sqrt{x^2+15}$

Evaluating for x=7

$(r\circ q)(7)=\sqrt{7^2+15}=\sqrt{64}=\pm 8$

We have two solutions

$\boxed{(r\circ q)(7)=8,\ (r\circ q)(7)=-8}$

Now compute

$(q\circ r)(x)=(\sqrt{x+9})^2+6=x+9+6=x+15$

For x=7

$(q\circ r)(7)=7+15=22$

$\boxed{(q\circ r)(7)=22}$