1. Let Find g(n) = —n + 7 and
h(n) = -3n + 2. Find (g.h) (2)

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!

Let Find g(n) = —n + 7 and h(n) = -3n + 2. Find (g.h)(2)

Solve the function composition problem where g(n) = -n + 7 and h(n) = -3n + 2. Learn how to find (g ∘ h)(2) step by step. This problem highlights key concepts in algebra and function composition. Suitable for students in Grades 9-12.

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