To find \((f + g)(3)\), we need to first find the sum of \(f(x)\) and \(g(x)\), and then evaluate it at \(x = 3\).

1. **Add the two functions:**

\[
(f + g)(x) = f(x) + g(x)
\]
Substituting the given functions:

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

Simplifying the expression:

\[
(f + g)(x) = 2x - 3x + 7 - 1 = -x + 6
\]

2. **Now, substitute \(x = 3\) into the expression for \((f + g)(x)\):**

\[
(f + g)(3) = -(3) + 6 = -3 + 6 = 3
\]

So, \((f + g)(3) = 3\).

Would you like more details or have any questions?

Here are some related questions for further practice:
1. Find \((f - g)(3)\) for the same functions.
2. Solve for \((f \cdot g)(3)\).
3. Determine \(\frac{f}{g}(3)\), if defined.
4. What is the domain of \((f + g)(x)\)?
5. Evaluate \((f + g)(x)\) for \(x = -2\).

**Tip:** When combining functions, always simplify the expression before substituting a specific value for \(x\).

Learn how to find (f+g)(3) for the given linear functions f(x) = 2x + 7 and g(x) = -3x - 1. This step-by-step guide explains the addition of functions and substitution method to simplify the expression. 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