https://file.aiquickdraw.com/mathbot/file/1727313306730e0lsilhq.jpg

The problem presented asks to determine \( g(g(x)) \) given two functions:

1. \( f(x) = x^2 - 3x + 2 \)
2. \( g(x) = 4x + 1 \)

To solve \( g(g(x)) \), we substitute the function \( g(x) \) into itself:

\[
g(g(x)) = g(4x + 1)
\]

Now, using the definition of \( g(x) \), replace \( x \) in \( g(x) \) with \( 4x + 1 \):

\[
g(4x + 1) = 4(4x + 1) + 1
\]

Expand the expression:

\[
g(4x + 1) = 16x + 4 + 1 = 16x + 5
\]

Thus, \( g(g(x)) = 16x + 5 \).

Would you like further details or explanations?

---

Here are five related questions to explore:

1. What is \( f(g(x)) \) if \( f(x) = x^2 - 3x + 2 \) and \( g(x) = 4x + 1 \)?
2. How would you find \( g(f(x)) \) with the same functions?
3. How can we determine the inverse of the function \( g(x) = 4x + 1 \)?
4. What is the derivative of \( g(g(x)) \)?
5. How would you solve for \( x \) if \( g(g(x)) = 0 \)?

**Tip**: For function composition, always substitute the inner function first before simplifying.

Jika f(x) = x² - 3x + 2 dan g(x) = 4x + 1, maka (g(g(x))) = _____.

Solve the function composition problem where f(x) = x² - 3x + 2 and g(x) = 4x + 1. Learn how to find g(g(x)) through step-by-step substitution, perfect 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