Instruction: Evaluate the following functions.
Let f(x) = x +1 g(x) = 3x -4

1. (f + g)(x) =

2. (f – g)(x) =

3. (f * g)(x) =

4. ( f
g
) (x) =

Given the functions \( f(x) = x + 1 \) and \( g(x) = 3x - 4 \), let's evaluate the following operations:

1. **\((f + g)(x)\):**
\[
(f + g)(x) = f(x) + g(x) = (x + 1) + (3x - 4) = x + 1 + 3x - 4 = 4x - 3
\]

2. **\((f - g)(x)\):**
\[
(f - g)(x) = f(x) - g(x) = (x + 1) - (3x - 4) = x + 1 - 3x + 4 = -2x + 5
\]

3. **\((f \times g)(x)\):**
\[
(f \times g)(x) = f(x) \cdot g(x) = (x + 1)(3x - 4) = 3x^2 - 4x + 3x - 4 = 3x^2 - x - 4
\]

4. **\(\left(\frac{f}{g}\right)(x)\):**
\[
\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{x + 1}{3x - 4}
\]

### Summary:
1. \((f + g)(x) = 4x - 3\)
2. \((f - g)(x) = -2x + 5\)
3. \((f \times g)(x) = 3x^2 - x - 4\)
4. \(\left(\frac{f}{g}\right)(x) = \frac{x + 1}{3x - 4}\)

Would you like more details or have any questions?

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Here are 5 related questions to deepen understanding:
1. What is the value of \((f + g)(2)\)?
2. What happens when you substitute \( x = 0 \) in \(\left(\frac{f}{g}\right)(x)\)?
3. How do the graphs of \( f(x) \) and \( g(x) \) compare?
4. Can you factorize \((f \times g)(x)\)?
5. What is the domain of \(\left(\frac{f}{g}\right)(x)\)?

**Tip**: Always check for restrictions in the domain when dividing functions. In \(\frac{f(x)}{g(x)}\), ensure the denominator \( g(x) \neq 0 \).

Evaluate the following functions. Let f(x) = x +1, g(x) = 3x -4

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

Learn how to evaluate function operations, including addition, subtraction, multiplication, and division, for f(x) = x + 1 and g(x) = 3x - 4. This problem covers core algebraic concepts and is suitable for students in Grades 9-11.

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