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The image contains a set of functions and operations related to composition, addition, subtraction, and other function manipulations. Here’s a breakdown of the problem based on what’s visible:

### GIVEN FUNCTIONS:
1. \( f(x) = -3x^2 + 5x - 4 \)
2. \( g(x) = \frac{x^2 - 1}{x - 5} \)
3. \( j(x) = -4x^2 + 3x + 9 \)
4. \( m(x) = x^3 - 4x - 5 \)
5. \( n(x) = 2x^4 - 18x^3 + 40x \)
6. \( c(x) = 2x - 32 \)
7. \( d(x) = \frac{3x^2}{5} + 3x + 5 \)
8. \( h(x) = \frac{8x^2 - 32x + 16}{x^2 - 7x + 10} \)

### PROBLEMS:
You are asked to perform various operations, such as additions, subtractions, and compositions of these functions. Here are a few examples of what's required:
1. \( (f + j)(x) \)
2. \( (f + m)(x) \)
3. \( (f + n)(x) \)
4. \( (j + m)(x) \)
5. \( (b + d)(x) \)
6. \( (b - d)(x) \)
7. \( (c - d)(x) \)
8. \( (b - c)(x) \)
9. \( (m \cdot n)(x) \)
10. \( (m \cdot c)(x) \)
11. \( (f \circ g)(x) \) (Composition of functions)
12. \( (g \circ f)(x) \)
13. \( (f \circ j)(x) \)
14. \( (j \circ f)(x) \)

Would you like to start solving these step by step? If so, I can guide you through specific problems or solve any of them directly. Let me know which one you'd like to start with!

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Here are five related questions to deepen understanding:
1. How do you simplify the composition of functions \( (f \circ g)(x) \)?
2. What is the process for adding two polynomial functions like \( f(x) + m(x) \)?
3. What rules govern the multiplication of two functions \( (m \cdot n)(x) \)?
4. How do you handle fractions when subtracting rational functions like \( \frac{b(x)}{d(x)} \)?
5. What happens when you substitute a function inside another, as with \( (g \circ f)(x) \)?

### Tip:
For function composition, remember to substitute the entire expression of one function into the other, replacing the variable \( x \).

Perform the indicated operations given the functions, including addition, subtraction, multiplication, and composition of functions. Examples include (f + j)(x), (f + m)(x), (m * n)(x), (f ∘ g)(x), etc.

Learn how to perform function operations such as addition, subtraction, multiplication, and composition with polynomial and rational functions. Explore key algebraic concepts like function composition and polynomial manipulation. Suitable for high school students in Grades 9-12.

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