Composite and Inverse Functions Introductory
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Composite and Inverse Functions Introductory — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionChecking if Two Functions Are InversesConcept Practice
2 marks~3 minCriterion C
A traveller flying from London to New York checks a weather app showing the forecast in Celsius. On arrival, all temperatures are displayed in Fahrenheit.

The conversion formulas are F=95C+32F = \dfrac{9}{5}C + 32 and C=59(F−32)C = \dfrac{5}{9}(F - 32).
a
Show that applying both formulas in succession to C=20C = 20 returns the original value. [1]
b
Advise the traveller whether these two formulas can be used reliably for temperature conversion in both directions. Justify your answer using the result from part (a). [1]
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Solutions

2QuestionChecking if Two Functions Are InversesAssessment Practice
4 marks~6 minCriterion D
A traveller converts euros to US dollars using f(x)=1.08xf(x) = 1.08x, then back to euros using g(x)=x1.08g(x) = \dfrac{x}{1.08}, where xx represents the amount in the respective currency.
a
Prove that ff and gg are inverse functions by computing f(g(x))f(g(x)) and g(f(x))g(f(x)). Show all steps. [2]
b
A bank applies a 2% fee on every conversion and rounds each result to the nearest cent. Advise the traveller whether ff and gg can be relied upon as exact inverses under these real banking conditions, justifying your answer with a specific numerical example. [2]
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3QuestionEvaluating Composite FunctionsAssessment Practice
5 marks~8 minCriterion A
A company models its profit P(t)P(t) (in thousands of dollars) using the composite function P(t)=R(C(t))P(t) = R(C(t)), where tt is time in years. The production cost function is C(t)=2t+5C(t) = 2t + 5 and the revenue function is R(x)=3x−4R(x) = 3x - 4, where xx represents production cost (both in thousands of dollars).
a
Evaluate P(5)P(5). [2]
b
The company considers a profit of at least 40 thousand dollars at t=5t = 5 to be financially viable. Justify whether this target is met. [1]
c
Discuss one strength and one limitation of using this composite function to forecast business profit. [2]
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4QuestionEvaluating Composite FunctionsAssessment Practice
6 marks~9 minCriterion B
A computer simulation models the spread of a digital signal through a network. At each step, the signal passes through two filters in sequence: filter ff doubles the strength, then filter gg adds 1 unit. Formally, f(x)=2xf(x) = 2x and g(x)=x+1g(x) = x + 1, giving composite function h(x)=g(f(x))h(x) = g(f(x)). The simulation begins at strength x0=1x_0 = 1 and updates by xn+1=h(xn)x_{n+1} = h(x_n).
a
Calculate x1x_1, x2x_2, x3x_3, and x4x_4. [2]
b
Deduce a general formula for xnx_n in terms of nn. [2]
c
The network has a maximum capacity of 1000 units. Justify whether this capacity is exceeded within the first 8 steps of the simulation. [2]

Solutions

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