Question

suppose that the functions q and r are defined as follows.
q(x) = -x
r(x) = x² + 2
find the following.
(r ∘ q)(-3) =
(q ∘ r)(-3) =

Explanation:

Step1: Compute $q(-3)$ first

$q(-3) = -(-3) = 3$

Step2: Substitute into $r(x)$ for $(r\circ q)(-3)$

$(r\circ q)(-3) = r(q(-3)) = r(3) = 3^2 + 2 = 9 + 2 = 11$

Step3: Compute $r(-3)$ first

$r(-3) = (-3)^2 + 2 = 9 + 2 = 11$

Step4: Substitute into $q(x)$ for $(q\circ r)(-3)$

$(q\circ r)(-3) = q(r(-3)) = q(11) = -11$

Answer:

$(r\circ q)(-3) = 11$
$(q\circ r)(-3) = -11$