Help with composite functions? Suppose that $u$ and $w$ are defined as follows: 
$u(x) = x^2 + 9$
$w(x) = \sqrt{x + 8}$
What is: 
$(u \circ w)(8) = $
$(w \circ u)(8) = $
I missed this in math class. Any help?

When the function isn’t too complicated, it may help to express it in words. So, your $u$ is “square the input, and then add $9$, to get your final output”. And your function $w$ is “add $8$ to your input, and then take the square root to get your final output”. And I’m sure you know that $u\circ w$ means to perform the $w$ process first, and then, using your output from $w$ as input to $u$, perform the $u$ process. That is exactly what @olive euler has done.
