Suppose that the functions $$ u $$ anc $$ \begin{array}{l}u(x)=x^{2}+7 \ w(x)=\sqrt{x+4} \ \text { Find the following. } \ (u \circ w)(5)=\square \ (w \circ u)(5)=\square\end{array} $$

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**Step 1. Calculate $$(u \circ w)(5)$$:**

- Compute $$w(5)$$:  
  $$
  w(5)=\sqrt{5+4}=\sqrt{9}=3
  $$

- Substitute into $$u(x)$$:  
  $$
  u(3)=3^2+7=9+7=16
  $$

Thus,  
$$
(u \circ w)(5)=16
$$

**Step 2. Calculate $$(w \circ u)(5)$$:**

- Compute $$u(5)$$:  
  $$
  u(5)=5^2+7=25+7=32
  $$

- Substitute into $$w(x)$$:  
  $$
  w(32)=\sqrt{32+4}=\sqrt{36}=6
  $$

Thus,  
$$
(w \circ u)(5)=6
$$
$$ (u \circ w)(5) = 16 \quad \text{and} \quad (w \circ u)(5) = 6 $$

Suppose that the functions anc

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