Question

suppose that the functions q and r are defined as follows.
q(x)=x² + 1
r(x)=√(x + 6)
find the following.
(r ∘ q)(3) =
(q ∘ r)(3) =

Explanation:

Step1: Solve $(r \circ q)(3)$: First find $q(3)$

$q(3) = 3^2 + 1 = 9 + 1 = 10$

Step2: Substitute $q(3)$ into $r(x)$

$(r \circ q)(3) = r(q(3)) = r(10) = \sqrt{10 + 6} = \sqrt{16} = 4$

Step3: Solve $(q \circ r)(3)$: First find $r(3)$

$r(3) = \sqrt{3 + 6} = \sqrt{9} = 3$

Step4: Substitute $r(3)$ into $q(x)$

$(q \circ r)(3) = q(r(3)) = q(3) = 3^2 + 1 = 9 + 1 = 10$

Answer:

$(r \circ q)(3) = 4$
$(q \circ r)(3) = 10$