https://file.aiquickdraw.com/mathbot/file/17265546272099x8l5l0z.jpg

The problem in the image asks to determine the composite function \( f \circ g(x) \) (fog \( x \)) where:

- \( f(x) = 3x + 1 \)
- \( g(x) = 9x - 2 \)

To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). This means wherever there is an \( x \) in \( f(x) \), we will replace it with \( g(x) \).

Here are the steps:

1. Start with the function \( f(x) = 3x + 1 \).
2. Replace \( x \) with \( g(x) \) which is \( 9x - 2 \). 

This gives us:
\[
f(g(x)) = 3(9x - 2) + 1
\]
Now, simplify the expression:
\[
f(g(x)) = 3 \cdot 9x - 3 \cdot 2 + 1 = 27x - 6 + 1 = 27x - 5
\]

Thus, the composite function \( f \circ g(x) \) is:
\[
f(g(x)) = 27x - 5
\]

Let me know if you need any more details or have questions!

Here are some related questions:
1. How do you find the composite function of \( g \circ f(x) \)?
2. What are the conditions for two functions to be invertible?
3. How does the order of composition affect the result of composite functions?
4. What happens when you compose a function with its inverse?
5. Can you have multiple solutions for a composite function?

**Tip:** When working with composite functions, always ensure you substitute carefully and simplify step by step to avoid errors.

Diketahui fungsi F(x) = 3x + 1, g(x) = 9x - 2. Tentukan rumus fungsinya f∘g(x).

Learn how to find the composite function f∘g(x) where f(x) = 3x + 1 and g(x) = 9x - 2. This problem covers key algebraic concepts like functions and composite functions. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation