https://file.aiquickdraw.com/mathbot/file/17261943685499nhytjml.jpg

From the image, you have the functions:

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

You are asked to find \( (f - g)(x) \), which means the difference between the two functions, i.e.,

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

Let's compute it:

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

Simplifying:

\[
(f - g)(x) = 3x + 3 + 4x - 1
\]
\[
(f - g)(x) = (3x + 4x) + (3 - 1)
\]
\[
(f - g)(x) = 7x + 2
\]

Thus, the result is:

\[
(f - g)(x) = 7x + 2
\]

Would you like more details or further explanation?

Here are five related questions to expand your understanding:
1. What is \( (f + g)(x) \) based on the given functions?
2. How would you find \( (f \cdot g)(x) \), the product of \( f(x) \) and \( g(x) \)?
3. How can you compute the composite function \( f(g(x)) \)?
4. What is the inverse of \( f(x) = 3x + 3 \)?
5. How do you find the x-intercept of \( (f - g)(x) \)?

**Tip:** When subtracting two functions, be sure to distribute the negative sign to all terms in the second function before simplifying.

Find (f - g)(x) where f(x) = 3x + 3 and g(x) = -4x + 1

Learn how to find the difference of two functions (f - g)(x) where f(x) = 3x + 3 and g(x) = -4x + 1. This problem demonstrates basic algebraic concepts including the subtraction of functions, combining like terms, and simplifying expressions. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation