Question

Suppose the functions q and r are defined as follows.
q(x)=x^2+6
r(x)=sqrtx+1
Find the following
(q degree r)(3)
(r degree q)(3)

Answer 1

To find (q degree r)(3), we need to substitute q(r(3)) into the expression for q.
First, we find r(3):
r(3) = sqrt(3) + 1
Next, we find q(r(3)):
q(r(3)) = q(sqrt(3) + 1)
= (sqrt(3) + 1)^2 + 6
= 3 + 2sqrt(3) + 1 + 6
= 10 + 2sqrt(3)

Therefore, (q degree r)(3) = 10 + 2sqrt(3).

To find (r degree q)(3), we need to substitute r(q(3)) into the expression for r.
First, we find q(3):
q(3) = 3^2 + 6
= 9 + 6
= 15
Next, we find r(q(3)):
r(q(3)) = r(15)
= sqrt(15) + 1

Therefore, (r degree q)(3) = sqrt(15) + 1.