Komposisi Fungsi Part 1 - Operasi Aljabar Pada Fungsi [ Matematika Wajib Kelas X ]

Introduction

This tutorial provides a step-by-step guide on the composition of functions, a fundamental concept in algebra. Understanding how to perform operations with functions is crucial for students, particularly in mathematics classes. This guide will help you grasp the principles of function composition and algebraic operations, relevant for Grade X mathematics.

Step 1: Understanding Functions

• Define what a function is: A relation where each input has exactly one output.
• Identify common notations for functions, such as f(x) and g(x).
• Recognize types of functions (linear, quadratic, etc.) and their characteristics.

Step 2: Learning Function Composition

• Understand the concept of function composition, which involves combining two functions.
• The notation for composing functions is (f ∘ g)(x) = f(g(x)).
• This means substituting the output of g(x) into the function f(x).

Practical Steps for Composition

1. Identify the functions you want to compose. For example, let f(x) = 2x + 3 and 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 if necessary.

Step 3: Performing Algebraic Operations on Functions

• Familiarize yourself with basic operations: addition, subtraction, multiplication, and division of functions.
• Use the following notations:
  • (f + g)(x) = f(x) + g(x)
  • (f - g)(x) = f(x) - g(x)
  • (f * g)(x) = f(x) * g(x)
  • (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Example of Algebraic Operations

1. Given f(x) = 2x + 3 and g(x) = x^2:
   • Addition: (f + g)(x) = (2x + 3) + (x^2) = x^2 + 2x + 3
   • Multiplication: (f * g)(x) = (2x + 3)(x^2) = 2x^3 + 3x^2

Step 4: Practice Problems

• Solve practice problems to reinforce your understanding of function composition and operations.
• Example Problem: If f(x) = x + 1 and g(x) = 3x, find (f ∘ g)(2).
  • Solution: g(2) = 3(2) = 6, then f(g(2)) = f(6) = 6 + 1 = 7.

Conclusion

In this guide, we explored the fundamentals of function composition and algebraic operations. We learned how to combine functions and perform various operations, enhancing our understanding of algebra. To further solidify these concepts, consider practicing with different functions and operations. For more advanced topics, explore additional resources on inverse functions and quadratic factorizations.