Suppose that the functions $$ p $$ and $$ q $$ are defined as follows. $$ \begin{array}{r}p(x)=x^{2}+9 \ q(x)=\sqrt{x+8}\end{array} $$ Find the following. $$ \begin{array}{l}(p \circ q)(8)=\square \ (q \circ p)(8)=\square\end{array} $$

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UpStudy AI · Accepted Answer

We start with the functions
$$
p(x) = x^2 + 9 \quad \text{and} \quad q(x) = \sqrt{x + 8}.
$$

1. To find $$(p \circ q)(8)$$, we first compute $$q(8)$$:
   $$
   q(8) = \sqrt{8 + 8} = \sqrt{16} = 4.
   $$
   Then, using the result for $$q(8)$$, we compute $$p(4)$$:
   $$
   p(4) = 4^2 + 9 = 16 + 9 = 25.
   $$
   Therefore, $$(p \circ q)(8) = 25$$.

2. To find $$(q \circ p)(8)$$, we first compute $$p(8)$$:
   $$
   p(8) = 8^2 + 9 = 64 + 9 = 73.
   $$
   Then, using the result for $$p(8)$$, we compute $$q(73)$$:
   $$
   q(73) = \sqrt{73 + 8} = \sqrt{81} = 9.
   $$
   Therefore, $$(q \circ p)(8) = 9$$.

The final answers are:
$$
(p \circ q)(8)=25 \quad \text{and} \quad (q \circ p)(8)=9.
$$
$$(p \circ q)(8) = 25$$ and $$(q \circ p)(8) = 9$$.

Suppose that the functions and are defined as follows.

Find the following.

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