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

Question

asked Jan 11, 2021 143k views

1 Answer

Eddy Hernandez · Answer 1 · 2021-01-16T02:00:00+0000

Answer:

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

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

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)=√(x+9)

Compute

$(r\circ q)(x)=√(x^2+6+9)=√(x^2+15)$

Evaluating for x=7

$(r\circ q)(7)=√(7^2+15)=√(64)=\pm 8$

We have two solutions

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

Now compute

$(q\circ r)(x)=(√(x+9))^2+6=x+9+6=x+15$

For x=7

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

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