IB Maths AI HL 2.7 Composite and inverse functions Question Bank

Practise IB Mathematics HL 2.7 by applying composite and inverse functions methods to exam-style questions.

[Maximum number: 4]

Walkea Tree is a furniture store. They offer a 30 % discount on all chairs priced over 250 Canadian dollars (CAD).
A different furniture store, LuxeCraft, offer customers a reduction of 150 CAD on all chairs priced over 250 CAD .

(a)

Describe the meaning of $(f \circ g)(x)$ , in context.

[ 2 ]

attempt to discuss the order in which the reduction/discount are applied
$(f \circ g)(x)$ describes when the 150 CAD reduction is applied before the 30 % discount.

(b)

State, with justification, whether $(f \circ g)(x)$ or $(g \circ f)(x)$ is better for the customer when they buy a chair with an original price of 450 CAD .

[ 2 ]

EITHER
evidence of solving $(f \circ g)(x)$ and $(g \circ f)(x)$ for a price at 450 CAD

OR
$(f \circ g)(x)=0.7 x-105$ and $(g \circ f)(x)=0.7 x-150$ seen

OR
stating that it is better for 30 % to be deducted from a higher price

OR
the numbers 165, 210 are seen

THEN
$(g \circ f)(x)$ is better for the customer

Note: Do not award R0A1.

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AHL 2.7 (HL)—Composite and inverse functions question 1

Question (a)

Question (b)