https://file.aiquickdraw.com/mathbot/file/172591776201808sq69gj.jpg

We are asked to find \( (f - g)(x) \), given the functions \( f(x) = -5x - 4 \) and \( g(x) = -3x - 2 \).

The difference between two functions \( f(x) \) and \( g(x) \) is calculated by subtracting the expressions for each:

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

Substitute the given functions for \( f(x) \) and \( g(x) \):

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

Now, simplify the expression by distributing the negative sign:

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

Combine like terms:

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

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

So, the correct answer is \( (f - g)(x) = -2x - 2 \), which corresponds to option **B**.

Would you like further explanation on any of these steps?

Here are 5 related questions to explore this topic further:
1. How do you add two functions, such as \( f(x) + g(x) \)?
2. What happens when you multiply two functions, \( f(x) \times g(x) \)?
3. How can you verify the result of subtracting two functions graphically?
4. What is the difference between \( f(g(x)) \) and \( f - g(x) \)?
5. Can the subtraction of functions ever result in a constant function?

**Tip**: When combining functions, always distribute any negative signs properly to avoid mistakes in simplification!

If f(x) = -5x - 4 and g(x) = -3x - 2, find (f - g)(x).

Learn how to find (f - g)(x) for the functions f(x) = -5x - 4 and g(x) = -3x - 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including function operations and linear functions, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation