FUNGSI KOMPOSISI dengan 3 fungsi

Summary

This video tutorial focuses on the concept of function composition with three leaf functions: f(x) = 2x - 9, g(x) = x^2 - 2x - 3, and h(x) = x + 4. The presenter guides viewers through solving three composition problems: h(g(f(x))), g(f(h(x))), and h(g(f(x))). Each step is carefully explained, with substitutions and calculations shown in detail, aiming to make the complex topic of function composition accessible and easy to understand.

Takeaways

• 📚 The video is an educational tutorial focused on the concept of function composition involving three leaf functions.
• 🔢 The functions discussed are f(x) = 2x - 9, g(x) = x^2 - 2x - 3, and h(x) = x + 4.
• 📝 The tutorial aims to solve the problem of finding the composition of these functions in different orders: h(g(f(x))), g(f(h(x))), and h(g(f(x))).
• 👨‍🏫 The presenter emphasizes the importance of following the order of functions when solving the compositions.
• 📈 The process involves substituting the inner functions into the outer functions step by step.
• 🧮 The tutorial includes detailed calculations for each composition, showing how to handle algebraic expressions.
• 📉 The presenter simplifies the expressions by combining like terms and performing arithmetic operations.
• 🔑 The tutorial provides a final answer for each function composition, demonstrating the result of the calculations.
• 📋 The presenter uses clear and step-by-step explanations to ensure viewers can follow along with the process.
• 🌟 The video concludes with a reminder to like, subscribe, and comment, and a hope that the video will be beneficial and a source of good deeds.

Q & A

What is the main topic discussed in the video?

The main topic discussed in the video is about function composition involving three leaf functions.

What are the three functions mentioned in the video?

The three functions mentioned are f(x) = 2x - 9, g(x) = x^2 - 2x - 3, and h(x) = x + 4.

What is the first composition of functions discussed in the video?

The first composition of functions discussed is f(g(h(x)) which involves substituting h(x) into g(x), and then the result into f(x).

How is h(x) defined in the video?

h(x) is defined as x + 4 in the video.

What is the process to find f(g(h(x))) as described in the video?

The process involves substituting h(x) into g(x) first, then substituting the result into f(x), and simplifying the expression step by step.

What is the final simplified expression for f(g(h(x)))?

The final simplified expression for f(g(h(x))) is 2x^2 + 12x + 10 - 9, which simplifies to x^2 + 6x + 1.

What is the second composition of functions discussed in the video?

The second composition of functions discussed is g(f(h(x))) which involves substituting h(x) into f(x), and then the result into g(x).

What is the final simplified expression for g(f(h(x)))?

The final simplified expression for g(f(h(x))) is 4x^2 - 4x - 4.

What is the third composition of functions discussed in the video?

The third composition of functions discussed is h(g(f(x))) which involves substituting f(x) into g(x), and then the result into h(x).

What is the final simplified expression for h(g(f(x)))?

The final simplified expression for h(g(f(x))) is 4x^2 - 40x + 96 + 4, which simplifies to 4x^2 - 40x + 100.

What is the advice given at the end of the video for understanding function compositions?

The advice given at the end of the video is to pay attention to the order of functions and to simplify the expressions step by step.