https://file.aiquickdraw.com/mathbot/file/1726106883313fokexb7c.jpg

The problem asks us to find \((g \circ f)(2)\), given the following functions:

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

The composition of functions \((g \circ f)(x)\) means that we first apply \(f(x)\) and then apply \(g\) to the result of \(f(x)\). In mathematical terms:

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

### Step 1: Find \(f(2)\)
Substitute \(x = 2\) into \(f(x)\):

\[
f(2) = 2(2) + 3 = 4 + 3 = 7
\]

### Step 2: Find \(g(f(2)) = g(7)\)
Now, substitute \(x = 7\) into \(g(x)\):

\[
g(7) = 3(7) - 2 = 21 - 2 = 19
\]

Thus, \((g \circ f)(2) = 19\).

### Answer: 
The correct choice is B. \(19\).

Do you have any further questions or need more details? Here are 5 related questions to expand on this concept:

1. How do you find the composition of two functions in general?
2. If \(f(x) = x^2 + 1\) and \(g(x) = x - 3\), what is \((g \circ f)(x)\)?
3. Can you reverse the composition, i.e., find \((f \circ g)(2)\) for the given functions?
4. What is the geometric interpretation of function composition?
5. What are some applications of function composition in real-life problems?

**Tip:** Always be careful with the order when composing functions—\((g \circ f)(x)\) is not the same as \((f \circ g)(x)\).

Diketahui fungsi f dan g yang dinyatakan oleh f(x) = 2x + 3 dan g(x) = 3x - 2. Maka (g o f)(2) = ...

Learn how to solve the function composition problem (g o f)(2), where f(x) = 2x + 3 and g(x) = 3x - 2. This example demonstrates how to apply algebraic techniques to solve for the composition of functions. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation