f(g(x)): Challenge & Extension
Mathematics
Grade 7
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concept of composite functions f(g(x)) with increasing difficulty, including practice, problem-solving, and extension questions.
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f(g(x)): Challenge & Extension
Subject: MathematicsGrade: Grade 7
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Date:
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Untitled Worksheet
Grade Grade 7
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given f(x) = 2x + 3 and g(x) = x - 4, find f(g(5)).
[2 marks]2.
If f(x) = x^2 + 1 and g(x) = 3x - 2, what is f(g(2))?
[2 marks]3.
Calculate the value of f(g(0)) where f(x) = 4 - x and g(x) = x/2.
[2 marks]4.
Plot the graph of y = 2x on the provided grid. (Student draws)
[1 mark]B
Fluency & Practice
Solve the following to develop procedural mastery of composite functions.
1.
If f(x) = 3x + 2 and g(x) = x - 1, find f(g(3)).
[2 marks]2.
Given f(x) = x^2 - 4 and g(x) = 2x + 1, evaluate f(g(2)).
[2 marks]3.
Calculate f(g(1)) where f(x) = 5x and g(x) = x + 3.
[2 marks]C
Problem Solving & Reasoning
Solve multi-step problems involving composite functions and explain your reasoning.
1.
If f(x) = x^2 and g(x) = 2x + 5, find the value of x such that f(g(x)) = 49. Show your working.
[3 marks]2.
Explain why f(g(x)) = g(f(x)) is generally not true for arbitrary functions f and g. Provide an example with specific functions.
[3 marks]D
Real-world Applications
Apply your understanding of f(g(x)) to real-world contexts.
1.
A car's fuel consumption (in liters) is modeled by f(x) = 0.05x^2 + 2, where x is the distance traveled in kilometers. The speed (g(x)) in km/h is given by g(x) = 60 + 0.1x. Find the total fuel consumption after traveling at speed g(100) km/h for 2 hours. (Use composite function to model).
[3 marks]E
Challenge & Extension
Tackle these advanced problems to deepen your understanding of composite functions.
1.
Given f(x) = x^3 - x and g(x) = 2x + 5, find the value of x such that f(g(x)) = 0. Show all steps.
[4 marks]2.
Construct a function h(x) such that h(x) = f(g(x)) where f(x) = x + 4 and g(x) = 3x - 1. Then, compute h(2).
[3 marks]F
Mixed Review
Answer the variety of questions below to review your understanding of f(g(x)).
1.
If f(x) = x/2 + 1 and g(x) = 4x - 3, evaluate f(g(5)).
[2 marks]2.
Construct the composition f(g(x)) for f(x) = x^2 and g(x) = x + 2. Simplify your result.
[3 marks]G
Error Analysis
Identify the mistake in the following student solution and correct it.
1.
A student claims that f(g(2)) = f(2g(2)). Given f(x) = x + 3 and g(x) = 2x, find and explain the error. Correct the mistake.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet