16. Given g(x) = x + 5 and h(x) = 2x - 3 what is (g + h) * (2)' ??

A. 7

B. 8

C. 10

D. 14

To solve the expression \((g + h)(2)\), we first need to determine what \(g(x) + h(x)\) is, and then substitute \(x = 2\) into the resulting expression.

### Step 1: Find \(g(x) + h(x)\)
Given:
\[
g(x) = x + 5
\]
\[
h(x) = 2x - 3
\]

Now, add \(g(x)\) and \(h(x)\):
\[
g(x) + h(x) = (x + 5) + (2x - 3)
\]

Combine like terms:
\[
g(x) + h(x) = x + 2x + 5 - 3 = 3x + 2
\]

### Step 2: Substitute \(x = 2\)
Now that we have \(g(x) + h(x) = 3x + 2\), substitute \(x = 2\) into this expression:
\[
(g + h)(2) = 3(2) + 2 = 6 + 2 = 8
\]

So, the correct answer is:

**B. 8**

Would you like further details or have any questions? 

Here are five related questions:
1. What is \(g(x) + h(x)\) when \(x = 0\)?
2. How would the result change if \(h(x)\) were defined as \(h(x) = 2x + 3\) instead?
3. What is the value of \(g(x) \cdot h(x)\) at \(x = 2\)?
4. How do you find the inverse of the function \(g(x)\)?
5. What is the value of \(h(x)\) when \(x = -1\)?

**Tip:** When combining functions, always remember to first add or subtract the functions before applying any specific values for \(x\).

Given g(x) = x + 5 and h(x) = 2x - 3, what is (g + h)(2)? A. 7 B. 8 C. 10 D. 14

Learn how to solve the function addition problem (g + h)(2) where g(x) = x + 5 and h(x) = 2x - 3. This problem covers fundamental algebraic concepts suitable for students in Grades 8-10. Follow the step-by-step solution to understand how to add functions and evaluate at a specific point.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation