Matematika X - Fungsi Komposisi part 1 : Relasi dan Pengertian Fungsi

Introduction

In this tutorial, we will explore the concepts of composition functions, relations, and the definition of functions based on the video from BIG Course. Understanding these mathematical principles is crucial for solving problems in algebra and calculus. This guide aims to break down the material into clear, actionable steps, making it easier for you to grasp these fundamental concepts.

Step 1: Understanding Functions

• A function is a relation between a set of inputs and a set of possible outputs.
• Each input is related to exactly one output.
• Common notation for a function is f(x), where x is the input and f(x) is the output.

Key Points:

• Domain: The set of all possible inputs (x-values).
• Range: The set of all possible outputs (f(x)-values).
• Example: For the function f(x) = 2x + 3, the domain can be all real numbers, while the range will also be all real numbers.

Step 2: Exploring Relations

• A relation is a set of ordered pairs, which can include inputs that correspond to multiple outputs.
• Not every relation is a function; for it to qualify as a function, each input must have a unique output.

Practical Tip:

• To determine if a relation is a function, use the vertical line test. If a vertical line intersects the graph of the relation at more than one point, it is not a function.

Step 3: Composing Functions

• Function composition is the process of applying one function to the results of another.
• If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) or f(g(x)).

Steps to Compose Functions:

1. Identify the two functions you want to compose.
2. Substitute the output of the second function into the first function.
3. Simplify the resulting expression.

Example:

• Let f(x) = x + 2 and g(x) = 3x.
• The composition f(g(x)) would be calculated as follows:
  • First, find g(x): g(x) = 3x.
  • Then, substitute into f: f(g(x)) = f(3x) = 3x + 2.

Step 4: Solving Composition Function Problems

• Start by understanding the problem statement.
• Identify the functions involved and their respective domains and ranges.
• Perform the composition step-by-step, ensuring to simplify where necessary.

Common Pitfalls:

• Forgetting to respect the domain of the functions when composing.
• Failing to simplify the final expression.

Conclusion

In this tutorial, we've covered the essentials of functions, relations, and function composition. By breaking down complex concepts into manageable steps, you can tackle related problems with confidence. Next, practice with different functions and relations to enhance your understanding. Remember, the key to mastering these topics is consistent practice and application.