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 functions \(f(x) = 3x + 3\) and \(g(x) = -4x + 1\), follow these steps:

### 1. Find \((f+g)(x)\):
\[
(f+g)(x) = f(x) + g(x)
\]
Substitute the given functions:
\[
(f+g)(x) = (3x + 3) + (-4x + 1)
\]
Combine like terms:
\[
(f+g)(x) = 3x - 4x + 3 + 1 = -x + 4
\]
So,
\[
(f+g)(x) = -x + 4
\]

### 2. Find \((f-g)(x)\):
\[
(f-g)(x) = f(x) - g(x)
\]
Substitute the given functions:
\[
(f-g)(x) = (3x + 3) - (-4x + 1)
\]
Distribute the negative sign:
\[
(f-g)(x) = 3x + 3 + 4x - 1
\]
Combine like terms:
\[
(f-g)(x) = 3x + 4x + 3 - 1 = 7x + 2
\]
So,
\[
(f-g)(x) = 7x + 2
\]

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

Would you like more details or have any questions?

Here are five related questions to further explore this topic:
1. How would you find \((f \times g)(x)\) using the same functions?
2. What is the graph of \((f+g)(x)\) and \((f-g)(x)\)?
3. How do you find the domain and range of \((f+g)(x)\) and \((f-g)(x)\)?
4. What happens if you divide \(f(x)\) by \(g(x)\) and find \(\frac{f}{g}(x)\)?
5. Can you solve for the values of \(x\) where \((f+g)(x) = 0\) and \((f-g)(x) = 0\)?

**Tip:** When combining functions, always simplify the expression by combining like terms to get the final result.

Learn how to find the sum and difference of two functions, f(x) = 3x + 3 and g(x) = -4x + 1. Understand the step-by-step process to calculate (f+g)(x) and (f-g)(x) using algebraic manipulation. Suitable for high school students studying functions.

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