FUNGSI KOMPOSISI dengan 3 fungsi

Matematika Hebat

17 Jan 202213:21

Summary

TLDRThis 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.