Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Recognise and use function notation such as f(x), f⁻¹(x), fg(x) and f²(x)
Learning Objective/s:
  • Describe the meaning of the notations f(x), f⁻¹(x), fg(x), f∘g(x) and f²(x).
  • Compute values of functions, their inverses, products, composites, and squares.
  • Explain the algebraic steps required to find an inverse function.
  • Apply function notation to solve a range of practice problems accurately.
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice questions
  • Graph paper, calculators and rulers
  • Whiteboard and markers
  • Set of function‑notation flashcards (optional)
 Introduction:
Begin with a quick recall of what a function is and why consistent notation matters. Ask students to share an example of f(x) they have used recently. Explain that today they will master reading and manipulating f(x), f⁻¹(x), fg(x), f∘g(x) and f²(x), and success will be shown by correctly evaluating and constructing these forms.
Lesson Structure:
  1. Do‑now (5'): Evaluate f(2) from a given linear function displayed on the board.
  2. Mini‑lecture (10'): Introduce/refresh each function notation with concise examples.
  3. Guided practice (12'): Step‑by‑step demonstration of finding an inverse function using the three‑step method.
  4. Collaborative activity (10'): In groups compute fg(x), f∘g(x) and f²(x) for supplied functions and present results.
  5. Independent practice (5'): Students attempt the four practice questions on their worksheet.
  6. Quick check (3'): Exit ticket – write one correct statement distinguishing f²(x) from f∘f(x).
Conclusion:
We reviewed the meanings of key function symbols and practiced evaluating, inverting, multiplying, composing, and squaring functions. For the exit ticket each learner wrote a concise explanation of why f²(x) differs from f∘f(x). Homework: complete an additional worksheet with function‑notation problems and prepare a real‑world example that can be modelled using a composite function.