IB Mathematics AHL 2.7 Composite functions AI HL Paper 1- Exam Style Questions- New Syllabus
Question
- TimberTrend gives a 30% discount.
- EliteHome gives a fixed reduction of 150 CAD.
- GrandStyle decides to apply both a 30% discount and a 150 CAD reduction on chairs priced over 250 CAD.
\( g(x) \) = final price at EliteHome after the 150 CAD reduction.
(ii) \( g(x) \).
Most-appropriate topic codes (IB Mathematics: Applications and Interpretation HL 2025):
• SL 2.2: Function notation and the concept of a function as a mathematical model— part (a)
▶️ Answer/Explanation
(a)
(i) 30% discount:
The customer pays 70% of the original price.
\( f(x) = 0.7x \) (or \( x – 0.3x \)).
\( \boxed{f(x) = 0.7x} \)
(ii) Fixed reduction of 150 CAD:
\( g(x) = x – 150 \).
\( \boxed{g(x) = x – 150} \)
(b)
\( (f \circ g)(x) = f(g(x)) \) means applying \( g \) first, then \( f \). In context: the 150 CAD reduction is taken off the original price, then a 30% discount is applied to the reduced amount.
“It represents the final price when the store first subtracts 150 CAD and then applies a 30% discount to the result.”
(c)
For \( x = 450 \):
\( (f \circ g)(450) = f(450 – 150) = f(300) = 0.7 \times 300 = 210 \) CAD.
\( (g \circ f)(450) = g(0.7 \times 450) = g(315) = 315 – 150 = 165 \) CAD.
Since \( 165 < 210 \), \( (g \circ f)(x) \) gives a lower final price.
\( \boxed{(g \circ f)(x)} \) is better because it results in a final price of 165 CAD, compared to 210 CAD from the other order.