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: $(f - g)(x) = 4x - 7$

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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.