https://file.aiquickdraw.com/mathbot/file/1725721995080ycc11zch.jpg

It seems like the image's text wasn't fully extracted as expected. Let me try a different method to analyze and respond to your exercise. I'll manually work through the exercises listed in the image based on what I can discern visually.

The exercises appear to be based on subtraction of functions. Here’s how to solve them:

### Exercises:
1. \( f(x) = 3x - 4 \) and \( g(x) = x^2 - 4x + 4 \). Find \( (f - g)(x) \).
2. \( f(x) = 2x + 1 \) and \( g(x) = x^2 - 4 \). Find \( (f - g)(x) \).

---

### Solution to Exercise 1:
We need to find \( (f - g)(x) = f(x) - g(x) \).

Given:  
\( f(x) = 3x - 4 \)  
\( g(x) = x^2 - 4x + 4 \)

Now subtract \( g(x) \) from \( f(x) \):

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

Simplify:

\[
(f - g)(x) = 3x - 4 - x^2 + 4x - 4
\]
\[
(f - g)(x) = -x^2 + 7x - 8
\]

### Solution to Exercise 2:
We need to find \( (f - g)(x) = f(x) - g(x) \).

Given:  
\( f(x) = 2x + 1 \)  
\( g(x) = x^2 - 4 \)

Now subtract \( g(x) \) from \( f(x) \):

\[
(f - g)(x) = (2x + 1) - (x^2 - 4)
\]

Simplify:

\[
(f - g)(x) = 2x + 1 - x^2 + 4
\]
\[
(f - g)(x) = -x^2 + 2x + 5
\]

---

Would you like me to explain any of the steps further?

Here are 5 questions related to function operations for further practice:
1. If \( f(x) = x^2 + 2x \) and \( g(x) = 3x + 1 \), find \( (f - g)(x) \).
2. Given \( f(x) = 5x - 6 \) and \( g(x) = x^2 - 2x + 1 \), find \( (f - g)(x) \).
3. If \( f(x) = 4x^2 + 2 \) and \( g(x) = x^2 - 1 \), what is \( (f - g)(x) \)?
4. For \( f(x) = 3x + 7 \) and \( g(x) = 2x^2 - 5x \), find \( (f - g)(x) \).
5. If \( f(x) = x^2 \) and \( g(x) = 2x \), find \( (f + g)(x) \) instead of \( (f - g)(x) \).

### Tip:
When subtracting functions, distribute the negative sign carefully across all terms in \( g(x) \).

Learn how to solve subtraction of functions with detailed steps. The exercises involve simplifying polynomials using the formula (f - g)(x) = f(x) - g(x). Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation