Pembahasan Latihan 1.3 Hal 23-24 Bab 1 KOMPOSISI FUNGSI DAN INVERS Kelas 11 SMA Kurikulum Merdeka

Introduction

This tutorial provides a step-by-step guide for understanding and solving exercises from pages 23-24 of Chapter 1 on Composition of Functions and Inverse Functions, as outlined in the Kurikulum Merdeka for 11th-grade mathematics. This guide is designed to help students grasp concepts and apply them in their exercises effectively.

Step 1: Understanding Functions

• Begin by reviewing the definition of a function:
  • A function relates each element of a set (domain) to exactly one element of another set (codomain).
• Familiarize yourself with key terms:
  • Domain: All possible input values.
  • Codomain: All possible output values.
  • Range: The actual output values produced.

Step 2: Composition of Functions

• Learn how to perform function composition:
  • If you have two functions, f(x) and g(x), their composition is written as (f ∘ g)(x) = f(g(x)).
• Follow these steps to compose functions:
  1. Identify the inner function (g(x)).
  2. Substitute the input of g into f.
  3. Simplify the result.

Example

If f(x) = 2x and g(x) = x + 3, then:

• (f ∘ g)(x) = f(g(x)) = f(x + 3) = 2(x + 3) = 2x + 6

Step 3: Solving Exercises on Page 23-24

• Review the specific exercises provided in your textbook.
• Apply the concepts of function composition:
  1. Read each problem carefully.
  2. Identify the functions involved.
  3. Compose the functions as needed.
  4. Solve the resulting expressions step-by-step.

Tips for Solving

• Always double-check your substitutions.
• Simplify expressions as much as possible.
• If stuck, refer back to the definitions and examples.

Step 4: Inverse Functions

• Understand the concept of an inverse function:
  • An inverse function reverses the effect of the original function.
  • If f(x) produces y, then f^(-1)(y) produces x.

How to Find Inverse Functions

1. Replace f(x) with y.
2. Swap x and y.
3. Solve for y to find f^(-1)(x).

Example

For f(x) = 3x + 1:

• Replace f(x) with y: y = 3x + 1
• Swap x and y: x = 3y + 1
• Solve for y: y = (x - 1)/3
• Thus, f^(-1)(x) = (x - 1)/3

Step 5: Practice Exercises

• After understanding the concepts, practice with additional exercises:
  • Find compositions and inverses for functions given in the textbook.
  • Work through problems systematically, applying the methods learned.

Conclusion

This tutorial highlights the key concepts of composition and inverse functions, along with practical steps to solve related exercises. To further enhance your understanding, continue practicing exercises from your textbook and review previous sections as needed. Consider discussing complex problems with peers or seeking help from teachers to solidify your knowledge.