Question

suppose that the functions u and w are defined as follows.
$u(x)=x^2 + 6$
$w(x)=sqrt{x + 9}$
find the following.
$(u \cdot w)(7) = $
$(w \cdot u)(7) = $

Explanation:

Step1: Compute $w(7)$

$w(7)=\sqrt{7+9}=\sqrt{16}=4$

Step2: Compute $(u \circ w)(7)=u(w(7))$

$u(4)=4^2 + 6=16+6=22$

Step3: Compute $u(7)$

$u(7)=7^2 + 6=49+6=55$

Step4: Compute $(w \circ u)(7)=w(u(7))$

$w(55)=\sqrt{55+9}=\sqrt{64}=8$

Answer:

$(u \circ w)(7)=22$
$(w \circ u)(7)=8$