Determine the sum and difference of each functions.                                  f(x)=5x-3 g(x)=x+4

Given the functions \( f(x) = 5x - 3 \) and \( g(x) = x + 4 \), we can determine their sum and difference as follows:

### Sum of the Functions
The sum of the functions \( f(x) \) and \( g(x) \) is given by:
\[
(f + g)(x) = f(x) + g(x)
\]
Substituting the given functions:
\[
(f + g)(x) = (5x - 3) + (x + 4)
\]
Combine like terms:
\[
(f + g)(x) = 5x + x - 3 + 4 = 6x + 1
\]
So, the sum of the functions is:
\[
(f + g)(x) = 6x + 1
\]

### Difference of the Functions
The difference of the functions \( f(x) \) and \( g(x) \) is given by:
\[
(f - g)(x) = f(x) - g(x)
\]
Substituting the given functions:
\[
(f - g)(x) = (5x - 3) - (x + 4)
\]
Distribute the negative sign and combine like terms:
\[
(f - g)(x) = 5x - 3 - x - 4 = 4x - 7
\]
So, the difference of the functions is:
\[
(f - g)(x) = 4x - 7
\]

### Final Results
- **Sum**: \((f + g)(x) = 6x + 1\)
- **Difference**: \((f - g)(x) = 4x - 7\)

Would you like details on these operations or have any questions?

### Related Questions
1. How do you find the product of two functions \( f(x) \) and \( g(x) \)?
2. What happens if you compose \( f(x) \) and \( g(x) \), i.e., find \( f(g(x)) \)?
3. What is the inverse of the function \( f(x) = 5x - 3 \)?
4. How do you graph the sum of two functions on the coordinate plane?
5. What is the domain and range of the function \( (f + g)(x) = 6x + 1 \)?
6. How do you determine if \( f(x) + g(x) \) is increasing or decreasing?
7. Can you find the intersection point of \( f(x) \) and \( g(x) \)?
8. What are the critical points of the function \( (f - g)(x) = 4x - 7 \)?

### Tip
When combining functions, always combine like terms carefully, and watch out for any signs that might change during subtraction.

Explore how to find the sum and difference of functions f(x) = 5x - 3 and g(x) = x + 4 step-by-step. Understand the formulas for combining functions and learn how to apply them effectively. Suitable for high school students studying algebra and function operations.

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