https://file.aiquickdraw.com/mathbot/file/1727064245121ux0cf5ob.jpg

The problem shown in your image involves finding the sum of two functions \( f(x) = 7x - 9 \) and \( g(x) = 5 - x \), and then simplifying their sum.

### Step-by-Step Solution:

We are given the two functions:
- \( f(x) = 7x - 9 \)
- \( g(x) = 5 - x \)

The sum of the functions is:
\[
(f + g)(x) = f(x) + g(x)
\]
Substitute the given functions:
\[
(f + g)(x) = (7x - 9) + (5 - x)
\]
Now, combine like terms:
\[
(f + g)(x) = 7x - x - 9 + 5
\]
\[
(f + g)(x) = 6x - 4
\]

Thus, the sum of the functions is:
\[
(f + g)(x) = 6x - 4
\]

Would you like details on further parts of the problem or clarification? Here are some questions to extend your understanding:

1. How would you find \( (f - g)(x) \)?
2. Can you determine \( (f \cdot g)(x) \) by multiplying \( f(x) \) and \( g(x) \)?
3. What happens if you need to divide \( f(x) \) by \( g(x) \)?
4. How would you find the domain of \( \frac{f(x)}{g(x)} \)?
5. How can the sum \( f(x) + g(x) \) change if either function changes form?

**Tip:** When combining functions, always be careful with the signs and distribution, especially when subtracting functions!

Find (f + g)(x) where f(x) = 7x - 9 and g(x) = 5 - x.

Learn how to find the sum of two functions f(x) = 7x - 9 and g(x) = 5 - x, simplifying to (f + g)(x) = 6x - 4. This step-by-step solution covers basic algebraic concepts such as function addition and combining like terms, suitable for 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