We are given two functions:

• $g(n) = -n + 7$
• $h(n) = -3n + 2$

To find $(g \circ h)(2)$, we first apply the function $h(n)$, and then substitute the result into $g(n)$.

Step 1: Find $h(2)$

We substitute $n = 2$ into $h(n)$: $h(2) = -3(2) + 2 = -6 + 2 = -4$

Step 2: Find $g(h(2)) = g(-4)$

Now substitute $h(2) = -4$ into $g(n)$: $g(-4) = -(-4) + 7 = 4 + 7 = 11$

Final answer:

$(g \circ h)(2) = 11$

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do we interpret the composition of functions geometrically?
2. What happens when we switch the order of composition: $h(g(n))$?
3. How do we find the inverse of a function like $g(n)$ or $h(n)$?
4. What is the domain of the composition $(g \circ h)(n)$?
5. Can the composition of two linear functions always be another linear function?

Tip: Always apply the innermost function first in function compositions!