KOMPOSISI Fungsi

Introduction

This tutorial will guide you through the concept of Function Composition, also known as Komposisi Fungsi, as explained in the educational video from Media Matematika. Understanding function composition is essential for students, particularly those in high school, as it connects to other mathematical concepts such as inverse functions. This guide aims to simplify the topic using real-life examples to facilitate learning.

Step 1: Understand the Basics of Functions

• A function is a relation that maps each input to exactly one output.
• Functions are often denoted by symbols such as f(x), g(x), etc.
• Familiarize yourself with the following terms:
  • Domain: The set of all possible input values.
  • Range: The set of all possible output values.

Step 2: Learn About Function Composition

• Function composition involves combining two functions to create a new function.
• It is denoted as (f ∘ g)(x), meaning you apply function g first and then function f.

How to Compute Function Composition

1. Identify the two functions you want to compose. For example, let:
   • f(x) = 2x + 3
   • g(x) = x^2
2. Substitute g(x) into f(x):
   • (f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3
3. Simplify the expression:
   • (f ∘ g)(x) = 2x^2 + 3

Step 3: Explore Real-World Applications

• Function composition can be applied in various fields, such as physics, economics, and engineering.
• For instance, if g represents the cost of producing x items and f represents the revenue generated from that cost, understanding the composition can help in making business decisions.

Step 4: Practice with Examples

• Try composing functions on your own to reinforce learning:
  • Let h(x) = 3x - 5 and find (h ∘ f)(x).
  • Steps:
    1. Compute h(f(x)) = h(2x + 3).
    2. Substitute and simplify.

Common Pitfalls to Avoid

• Confusing the order of operations in function composition. Remember, f(g(x)) is not the same as g(f(x)).
• Not checking the domains of the composed functions, which can lead to undefined results.

Conclusion

Function composition is a powerful tool in mathematics, connecting various functions to solve problems effectively. By understanding the basics, practicing compositions, and applying them to real-world scenarios, you can enhance your mathematical skills. Continue to explore functions and their applications, and don't hesitate to ask your teachers for assistance when needed. Happy learning!