II. Task 3: Let x represent the regular price of the book a. Give a function f that represents the price of the book if a P100 price reduction applies b. Give a function g that represents the price of the book if a 10% discount applies. c. Compute (f@g)(x) and (g@f)(x) . Describe what these means. Which of the composition of functions give a better deal to the customer?

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II. Task 3: Let x represent the regular price of the book a. Give a function f that represents the price of the book if a P100 price reduction applies b. Give a function g that represents the price of the book if a 10% discount applies. c. Compute (f@g)(x) and (g@f)(x) . Describe what these means. Which of the composition of functions give a better deal to the customer?

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Answer 1

1. \( f(x) = x - 100 \)
2. \( g(x) = 0.9x \)
3. \( (f \circ g)(x) = -100 + 0.9x \)
4. \( (g \circ f)(x) = 0.9(x - 100) \)
5. \( (f \circ g)(x) \) gives a better deal to the customer.

Answer 2

1. The function \( f \) represents the price of the book after a P100 price reduction. This means that from the regular price \( x \), P100 is subtracted. Hence, \( f(x) = x - 100 \).
2. The function \( g \) represents the price of the book after a 10% discount. This means that the customer pays only 90% of the regular price \( x \). Hence, \( g(x) = 0.9x \).
3. The composition \( (f \circ g)(x) \) represents applying the 10% discount first and then subtracting P100. This results in \( -100 + 0.9x \).
4. The composition \( (g \circ f)(x) \) represents subtracting P100 first and then applying the 10% discount. This results in \( 0.9(x - 100) \).
5. To determine which composition gives a better deal to the customer, we need to compare the two compositions. Since \( -100 + 0.9x \) is less than \( 0.9(x - 100) \) for all positive values of \( x \), \( (f \circ g)(x) \) gives a better deal to the customer.

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