Question

suppose that the functions $p$ and $q$ are defined as follows.
$p(x)=x^{2}+4$
$q(x)=\sqrt{x+5}$
find the following.
$(q \cdot p)(4) = \square$
$(p \cdot q)(4) = \square$

Explanation:

Step1: Compute $p(4)$

$p(4)=4^2 + 4=16+4=20$

Step2: Compute $(q\circ p)(4)=q(p(4))$

$q(20)=\sqrt{20+5}=\sqrt{25}=5$

Step3: Compute $q(4)$

$q(4)=\sqrt{4+5}=\sqrt{9}=3$

Step4: Compute $(p\circ q)(4)=p(q(4))$

$p(3)=3^2 + 4=9+4=13$

Answer:

$(q \circ p)(4)=5$
$(p \circ q)(4)=13$