https://file.aiquickdraw.com/mathbot/file/1727312585136tfzk37ww.jpg

The image contains a mathematical problem written in Indonesian. It reads:

- "Jika \( f(x) = 4x - 3 \) dan \( g(x) = x + 6 \), maka rumus \( (f \circ g)(x) = 4x + 21 \)."

This is asking for the composition of two functions, \( f(x) \) and \( g(x) \), where:

- \( f(x) = 4x - 3 \)
- \( g(x) = x + 6 \)

To find the composition \( (f \circ g)(x) \), we substitute \( g(x) \) into \( f(x) \):

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

1. Start by substituting \( g(x) = x + 6 \) into the function \( f(x) = 4x - 3 \):

\[
f(g(x)) = 4(g(x)) - 3 = 4(x + 6) - 3
\]

2. Now, simplify the expression:

\[
= 4x + 24 - 3 = 4x + 21
\]

Thus, the correct formula for \( (f \circ g)(x) \) is:

\[
(f \circ g)(x) = 4x + 21
\]

This matches the given result.

Would you like any further explanation or details?

Here are five related questions to explore further:
1. How do you compute the composition of two functions in general?
2. What is the domain of the composition of two functions?
3. How does the result of \( f(g(x)) \) change if \( g(x) \) is a quadratic function?
4. What happens if you reverse the composition, i.e., calculate \( (g \circ f)(x) \)?
5. How does composition relate to inverse functions?

**Tip:** When performing function composition, always substitute the inner function into the outer function carefully, paying attention to signs and parentheses.

Jika f(x) = 4x - 3 dan g(x) = x + 6 maka rumus (f o g)(x) = 4x + 21

Learn how to compute the composition of two functions, f(x) = 4x - 3 and g(x) = x + 6, resulting in (f o g)(x) = 4x + 21. This algebra problem is suitable for students in Grades 9-12, covering key concepts of function composition and simplifying expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation