Question

suppose that the functions p and q are defined as follows.
p(x)=x² +3
q(x)=√(x+2)
find the following.
your answer
(q ∘ p)(2) =
(p ∘ q)(2) =

Explanation:

Step1: Find \( (q \circ p)(2) \)

First, recall that \( (q \circ p)(x) = q(p(x)) \). So we need to find \( p(2) \) first, then substitute that into \( q(x) \).

Calculate \( p(2) \):
\( p(2) = 2^2 + 3 = 4 + 3 = 7 \)

Now substitute \( p(2) = 7 \) into \( q(x) \):
\( q(7) = \sqrt{7 + 2} = \sqrt{9} = 3 \)

Step2: Find \( (p \circ q)(2) \)

Recall that \( (p \circ q)(x) = p(q(x)) \). So we need to find \( q(2) \) first, then substitute that into \( p(x) \).

Calculate \( q(2) \):
\( q(2) = \sqrt{2 + 2} = \sqrt{4} = 2 \)

Now substitute \( q(2) = 2 \) into \( p(x) \):
\( p(2) = 2^2 + 3 = 4 + 3 = 7 \)

Answer:

\( (q \circ p)(2) = \boldsymbol{3} \)
\( (p \circ q)(2) = \boldsymbol{7} \)