let F(x)=2x-5                                                                                                                                                                                                                                                                                
     g(x)=7-3x                                                                                                                                                                                          
     h(x)=4-3x+x^2                                                                                                                                                                                                                                                  f(-5), g(2), h(-3), g(h(-3)), f(f(-2)), f(a+b), g(g(x))

Let's evaluate each function step by step based on the given information:

### Given:
- \( F(x) = 2x - 5 \)
- \( g(x) = 7 - 3x \)
- \( h(x) = 4 - 3x + x^2 \)

### 1. \( f(-5) \)
Substitute \( x = -5 \) into \( F(x) = 2x - 5 \):
\[
f(-5) = 2(-5) - 5 = -10 - 5 = -15
\]

### 2. \( g(2) \)
Substitute \( x = 2 \) into \( g(x) = 7 - 3x \):
\[
g(2) = 7 - 3(2) = 7 - 6 = 1
\]

### 3. \( h(-3) \)
Substitute \( x = -3 \) into \( h(x) = 4 - 3x + x^2 \):
\[
h(-3) = 4 - 3(-3) + (-3)^2 = 4 + 9 + 9 = 22
\]

### 4. \( g(h(-3)) \)
First, find \( h(-3) \) (already calculated above):
\[
h(-3) = 22
\]
Now substitute \( x = 22 \) into \( g(x) = 7 - 3x \):
\[
g(22) = 7 - 3(22) = 7 - 66 = -59
\]

### 5. \( f(f(-2)) \)
First, find \( f(-2) \):
\[
f(-2) = 2(-2) - 5 = -4 - 5 = -9
\]
Now substitute \( x = -9 \) into \( F(x) = 2x - 5 \):
\[
f(f(-2)) = f(-9) = 2(-9) - 5 = -18 - 5 = -23
\]

### 6. \( f(a+b) \)
Substitute \( x = a + b \) into \( F(x) = 2x - 5 \):
\[
f(a+b) = 2(a + b) - 5 = 2a + 2b - 5
\]

### 7. \( g(g(x)) \)
First, find \( g(x) = 7 - 3x \).
Now substitute \( g(x) \) into \( g \) again:
\[
g(g(x)) = g(7 - 3x) = 7 - 3(7 - 3x) = 7 - 21 + 9x = -14 + 9x
\]

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### Final answers:
1. \( f(-5) = -15 \)
2. \( g(2) = 1 \)
3. \( h(-3) = 22 \)
4. \( g(h(-3)) = -59 \)
5. \( f(f(-2)) = -23 \)
6. \( f(a+b) = 2a + 2b - 5 \)
7. \( g(g(x)) = -14 + 9x \)

Would you like further clarification on any of these? 

---

### Related Questions:
1. What is \( h(g(x)) \)?
2. What is \( f(f(f(-1))) \)?
3. Can we evaluate \( h(f(x)) \) for a specific value of \( x \)?
4. How do you find the inverse of \( g(x) \)?
5. What is the general form of \( f(x) + g(x) \)?

#### Tip:
When substituting values into functions, simplify the inner functions first before proceeding to the outer ones (like with \( g(h(x)) \)).

let F(x)=2x-5 g(x)=7-3x h(x)=4-3x+x^2 f(-5), g(2), h(-3), g(h(-3)), f(f(-2)), f(a+b), g(g(x))

Learn how to evaluate functions F(x) = 2x - 5, g(x) = 7 - 3x, and h(x) = 4 - 3x + x^2, and solve composite functions like g(h(-3)) and f(f(-2)). This problem covers key algebraic concepts, including function evaluation and composition, suitable for students in Grades 9-11.

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