IB Maths AI HL Ahl 2 7 Hl Composite and Inverse Functions Questions

Practise evaluating composite functions, constructing inverses with domain restrictions, verifying by composition and interpreting input and output roles.

Exam points

Evaluate composite functions by substituting the inner function in the stated order and compare the result with the reverse composition.
Find an inverse by interchanging input and output, then impose and state the domain restriction needed for one-to-one behaviour.
Verify the inverse through composition and interpret the input/output roles in the model.

[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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IB Maths AI HL Ahl 2 7 Hl Composite and Inverse Functions Questions question 1

Question (a)

Question (b)