You have provided two functions:

- \( f(x) = x + 3 \)
- \( g(x) = 2x - 5 \)

Here are some common operations we can perform with these functions:

### 1. **Sum of the Functions**: 
\[ (f + g)(x) = f(x) + g(x) = (x + 3) + (2x - 5) = 3x - 2 \]

### 2. **Difference of the Functions**: 
\[ (f - g)(x) = f(x) - g(x) = (x + 3) - (2x - 5) = -x + 8 \]

### 3. **Product of the Functions**: 
\[ (f \cdot g)(x) = f(x) \cdot g(x) = (x + 3)(2x - 5) = 2x^2 - 5x + 6x - 15 = 2x^2 + x - 15 \]

### 4. **Quotient of the Functions**: 
\[ \left( \frac{f}{g} \right)(x) = \frac{f(x)}{g(x)} = \frac{x + 3}{2x - 5} \]

### 5. **Composite Functions**: 
- \( (f \circ g)(x) = f(g(x)) = f(2x - 5) = (2x - 5) + 3 = 2x - 2 \)
- \( (g \circ f)(x) = g(f(x)) = g(x + 3) = 2(x + 3) - 5 = 2x + 6 - 5 = 2x + 1 \)

Would you like more details on any of these operations?

### Follow-up Questions:
1. What is the inverse of \( f(x) \) and \( g(x) \)?
2. How do the graphs of \( f(x) \) and \( g(x) \) differ?
3. What are the zeros of \( f(x) \) and \( g(x) \)?
4. Can you find the domain and range of both functions?
5. How do you solve \( f(x) = g(x) \)?

**Tip**: Composite functions combine two functions by using the output of one as the input for the other—this is useful for modeling processes where one step depends on another.

Explore the operations on functions f(x) = x + 3 and g(x) = 2x - 5, including their sum, difference, product, quotient, and composite functions. Suitable for high school students, this page covers key algebraic concepts with step-by-step explanations.

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