(Part 4) FUNGSI KOMPOSISI FUNGSI INVERS KURIKULUM MERDEKA MATEMATIKA SMA KELAS 11 #matematikasma

Introduction

This tutorial focuses on understanding composite functions and inverse functions as part of the Merdeka Curriculum for 11th-grade mathematics. It will guide you through a practical example involving discount calculations, helping you determine which discount option is more beneficial for consumers.

Step 1: Understanding Composite Functions

Composite functions involve combining two functions to produce a new function. In this context, we will examine two discount options to see how they affect the final price of a product.

Key Points:

• A composite function is represented as (f ∘ g)(x), meaning you apply function g first and then function f.
• In the discount scenario, we will define two functions:
  • Function f: Applying a discount of 20%
  • Function g: Subtracting a fixed amount (e.g., Rp25,000)

Step 2: Analyzing the Discounts

Let’s break down the two discount options provided by the store.

Option 1: Discount First

1. Calculate the price after the 20% discount.
   • If the original price is P, the price after discount is:

     Price_after_discount = P - (0.20 * P) = 0.80 * P
     

2. Apply the additional Rp25,000 discount.
   • Final price:

     Final_price_1 = 0.80 * P - 25,000
     

Option 2: Fixed Discount First

1. Subtract the fixed discount from the original price.
   • Price after the fixed discount:

     Price_after_fixed_discount = P - 25,000
     

2. Then calculate the price after the 20% discount on the new price.
   • Final price:

     Final_price_2 = (P - 25,000) - (0.20 * (P - 25,000))
                     = 0.80 * (P - 25,000) 
                     = 0.80 * P - 20,000
     

Step 3: Comparing the Final Prices

Now that we have the final prices for both options, we can compare them.

Formulas to Compare:

• From Option 1:

  Final_price_1 = 0.80 * P - 25,000
  

• From Option 2:

  Final_price_2 = 0.80 * P - 20,000
  

Conclusion from Comparison:

• By comparing the two final prices:
  • If you analyze the constants, you’ll see that Final_price_1 will always be lower than Final_price_2 by Rp5,000.
• Therefore, Option 1 (discount first, then fixed amount) is more beneficial for the consumer.

Conclusion

In this tutorial, we explored composite functions through a practical discount scenario. We calculated two different discount methods and established that applying the percentage discount before the fixed discount yields a better price.

You can apply this understanding of composite functions not only in mathematics but also in real-life scenarios involving discounts and promotions. Next, try creating your own examples to further solidify your understanding of composite and inverse functions.