Komposisi Fungsi Himpunan Pasangan Berurutan - Matematika Wajib Kelas XI Kurikulum Merdeka

Introduction

This tutorial provides a comprehensive guide to understanding the composition of functions in mathematics, focusing specifically on ordered pairs as part of the curriculum for XI grade students in the Merdeka curriculum. By following these steps, you will learn how to work with functions, their composition, and the significance of ordered pairs in this context.

Step 1: Understand Functions and Ordered Pairs

• A function is a relation that uniquely associates each element from a set (domain) with one element from another set (codomain).
• Ordered pairs are typically written as (x, y), where:
  • x is from the domain.
  • y is from the codomain.
• Recognize that a function can be represented using ordered pairs, which illustrate the relationship between inputs and outputs.

Practical Tip

Familiarize yourself with the concepts of domain, codomain, and range to better understand how functions operate.

Step 2: Learn About Function Composition

• Composition of functions combines two functions to create a new function.
• If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x), which means you apply g first and then f.
• The formula to express this is:
  • (f ∘ g)(x) = f(g(x))

Common Pitfall

Ensure you apply the functions in the correct order; switching them can lead to different results.

Step 3: Apply Composition to Ordered Pairs

• To find the composition of functions represented by ordered pairs:
  1. Identify the output of the inner function from the input.
  2. Use this output as the input for the outer function.
• Example:
  • Let f = {(1, 2), (2, 3)} and g = {(2, 5), (3, 4)}.
  • To find (f ∘ g)(1):
    • First, find g(1). Since 1 is not in the domain of g, you cannot proceed.
    • Now, find (f ∘ g)(2):
      • g(2) = 5, then f(5) is not defined; thus, it doesn't yield a result.

Practical Application

Use a set of ordered pairs to practice composing functions. Create visual aids like charts or tables to help you understand how each output feeds into the next function.

Step 4: Explore Inverse Functions

• An inverse function reverses the effect of the original function.
• If f(x) = y, then the inverse function f^(-1)(y) = x.
• Understanding inverses is crucial when studying function composition since it helps clarify relationships between pairs.

Real-World Example

Consider a scenario where f represents the price of an item based on quantity purchased, and g represents the tax applied. The composition gives you the total cost, factoring in both functions.

Conclusion

Understanding the composition of functions and how ordered pairs fit into this concept is essential for mastering mathematical relationships. Practice with various functions and their compositions will enhance your comprehension. Consider exploring related topics like inverse functions and their applications as next steps in your learning journey. For more in-depth study, refer to additional resources on function definitions and examples.