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The uploaded image contains various mathematical exercises and notes. Here's an overview of what is covered:

1. **Equation Evaluation**:
   The function \( y = \frac{x+4}{x+2} \) is evaluated at \( x = \frac{1}{2} \).
   - First, the function is written as \( y = \frac{x+4}{x+2} \).
   - Substituting \( x = \frac{1}{2} \) gives:
     \[
     y = \frac{\frac{1}{2} + 4}{\frac{1}{2} + 2} = \frac{\frac{9}{2}}{\frac{5}{2}} = \frac{9}{5}
     \]
   - The final result is simplified to \( y = \frac{33}{15} \), but there is also an equivalent result of \( \frac{9}{5} \).

2. **Function Evaluation**:
   The function \( f(x) = 2x^2 + 4x \) is evaluated at \( x = 4 \).
   - \( f(4) = 2(4)^2 + 4(4) = 2(16) + 16 = 32 + 16 = 48 \), and another calculation gives the result \( 36 \).

3. **Another Function Evaluation**:
   The function \( f(x) = 2x^2 + 3 \) is evaluated at \( x = 3 \):
   - \( f(3) = 2(3)^2 + 3 = 2(9) + 3 = 18 + 3 = 21 \).

4. **Symbol Definitions**:
   - There’s a box listing symbols commonly used in mathematical logic and set theory:
     - \( = \) means "equal"
     - \( < \) means "less than"
     - \( \leq \) means "less than or equal to"
     - \( \in \) means "belongs to"
     - \( \therefore \) means "therefore"
     - \( \forall \) means "for all"
     - \( \in \) means "belongs to"
     - \( \Rightarrow \) means "implies"
     - \( [a, b] \) is a closed interval (includes the endpoints)
     - \( (a, b) \) is an open interval (excludes the endpoints)

### Any specific part you'd like further clarification on or detailed explanations?

### Related Questions:
1. What is the difference between open and closed intervals?
2. How do you simplify fractions like \( \frac{33}{15} \)?
3. Can you explain why the result for \( f(4) \) is 36 and not 48?
4. How do you evaluate a function at a given value of \( x \)?
5. What is the significance of the symbols \( \forall \) and \( \Rightarrow \) in logic?

### Tip:
When evaluating functions or solving equations, always double-check your substitutions and operations to avoid calculation errors.

Evaluate the function y = (x + 4) / (x + 2) for x = 1/2, and solve f(x) = 2x^2 + 4x and f(x) = 2x^2 + 3 at x = 4 and x = 3, respectively. Also, define the mathematical symbols listed.

This page explains how to evaluate the rational function y = (x + 4) / (x + 2) at x = 1/2 and solve the quadratic functions f(x) = 2x^2 + 4x and f(x) = 2x^2 + 3 at x = 4 and x = 3, respectively. It also provides a list of important mathematical symbols used in algebra.

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