Find (f+g)(x) and (f-g)(x) using two functions given in each number.

1. f(x)=3x+3 g(x)=-4x+1

To find \((f+g)(x)\) and \((f-g)(x)\) using the given functions \(f(x)\) and \(g(x)\), we perform the following operations:

### 1. Given Functions:
- \(f(x) = 3x + 3\)
- \(g(x) = -4x + 1\)

### \((f+g)(x)\):
\[
(f+g)(x) = f(x) + g(x)
\]
Substitute the expressions for \(f(x)\) and \(g(x)\):
\[
(f+g)(x) = (3x + 3) + (-4x + 1)
\]
Simplify:
\[
(f+g)(x) = 3x - 4x + 3 + 1 = -x + 4
\]

### \((f-g)(x)\):
\[
(f-g)(x) = f(x) - g(x)
\]
Substitute the expressions for \(f(x)\) and \(g(x)\):
\[
(f-g)(x) = (3x + 3) - (-4x + 1)
\]
Simplify:
\[
(f-g)(x) = 3x + 3 + 4x - 1 = 7x + 2
\]

### Final Answers:
- \((f+g)(x) = -x + 4\)
- \((f-g)(x) = 7x + 2\)

Would you like more details or have any questions? 

Here are some related questions:

1. How do you find \((f \cdot g)(x)\) using the given functions?
2. What is \((f/g)(x)\) for these functions?
3. How would \((f+g)(x)\) change if \(g(x)\) was a quadratic function?
4. What is the value of \((f+g)(2)\)?
5. How would the process differ if \(f(x)\) and \(g(x)\) were trigonometric functions?
6. What is the graphical interpretation of \((f+g)(x)\)?
7. Can you express \(f(x)\) and \(g(x)\) as a single combined function?
8. What is the domain of the function \((f-g)(x)\)?

**Tip:** When combining functions, always simplify the expression to its most reduced form for clarity.

Learn how to find (f+g)(x) and (f-g)(x) using the given functions f(x)=3x+3 and g(x)=-4x+1. This problem covers operations on functions, including addition and subtraction. Suitable for students in Grades 10-12.

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