The problem provides the function $g(n) = n^2 + 8$ and asks for $g(p - 9)$.

Solution:

1. Substitute $n = p - 9$ into the function: $g(p - 9) = (p - 9)^2 + 8$

2. Expand $(p - 9)^2$: $(p - 9)^2 = p^2 - 18p + 81$

3. Substitute back and simplify: $g(p - 9) = p^2 - 18p + 81 + 8$ $g(p - 9) = p^2 - 18p + 89$

Answer:

$g(p - 9) = p^2 - 18p + 89$

Would you like more details on this solution or have any questions?

Related Questions:

1. What is the process for expanding binomials like $(p - 9)^2$?
2. How would the answer change if the function was $g(n) = n^2 - 8$?
3. How do you find $g(a + b)$ if $g(n) = n^2 + c$ for a constant $c$?
4. What if $g(n) = 2n^2 + 3n + 5$; how would $g(p - 9)$ change?
5. Can you provide another example with different values substituted in $n$?

Tip:

When substituting variables, carefully expand and simplify expressions to avoid errors in algebraic manipulation.