https://file.aiquickdraw.com/mathbot/file/17255946652492l3rl3vh.jpg

The problem in the image asks to perform operations on given functions \( f(x) \), \( g(x) \), and \( h(x) \). The functions provided are:

- \( f(x) = x^2 - 3x + 4 \)
- \( g(x) = 5x + 2 \)
- \( h(x) = 6x \)

Let's perform the operations for parts **a** and **b**:

### a. \( (f + g)(x) \)
This means we need to add the two functions \( f(x) \) and \( g(x) \):

\[
(f + g)(x) = f(x) + g(x)
\]

Substituting the given functions:

\[
(f + g)(x) = (x^2 - 3x + 4) + (5x + 2)
\]

Now, combine like terms:

\[
(f + g)(x) = x^2 + (-3x + 5x) + (4 + 2)
\]

\[
(f + g)(x) = x^2 + 2x + 6
\]

### b. \( (f - g)(x) \)
This means we need to subtract the function \( g(x) \) from \( f(x) \):

\[
(f - g)(x) = f(x) - g(x)
\]

Substituting the given functions:

\[
(f - g)(x) = (x^2 - 3x + 4) - (5x + 2)
\]

Distribute the negative sign and combine like terms:

\[
(f - g)(x) = x^2 - 3x + 4 - 5x - 2
\]

\[
(f - g)(x) = x^2 + (-3x - 5x) + (4 - 2)
\]

\[
(f - g)(x) = x^2 - 8x + 2
\]

### Summary:
- \( (f + g)(x) = x^2 + 2x + 6 \)
- \( (f - g)(x) = x^2 - 8x + 2 \)

Would you like more details or have any questions? 

Here are 5 related questions:
1. How do you find the product of two functions, such as \( (f \times g)(x) \)?
2. What is the composition of two functions, such as \( (f \circ g)(x) \)?
3. How would the operation \( (f + h)(x) \) look?
4. Can you calculate \( (g - h)(x) \)?
5. How do you simplify \( (f \times g)(x) \)?

**Tip**: Always combine like terms when performing function addition or subtraction!

Perform the indicated operation with the functions given: f(x) = x^2 - 3x + 4, g(x) = 5x + 2, and h(x) = 6x. Find (f + g)(x) and (f - g)(x).

Learn how to perform function operations by adding and subtracting the functions f(x) = x^2 - 3x + 4 and g(x) = 5x + 2. This example demonstrates key algebraic concepts of combining like terms for Grades 8-10.

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