Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Find the inverse of a one–one function using correct notation
Learning Objective/s:
  • Describe the conditions that make a function one‑one and why this is required for an inverse.
  • Apply the step‑by‑step procedure to find $f^{-1}(x)$ for linear, rational and restricted‑domain functions.
  • State and justify the domain and range of the inverse function.
  • Verify an inverse by composition $f^{-1}(f(x))=x$.
Materials Needed:
  • Whiteboard and markers
  • Projector with slides of examples and graphs
  • Student worksheets with practice questions
  • Graph paper or digital graphing tool
  • Calculator (optional)
 Introduction:
Begin with a quick “guess the inverse” challenge using a simple linear function to spark curiosity. Review the definition of a function and the concept of one‑one (injective) mappings. Explain that today’s success criteria are: correctly find the inverse, label its domain and range, and check the result by composition.
Lesson Structure:
  1. Do‑Now (5 '): Students complete a short task swapping $x$ and $y$ for $y=2x-3$ on a slip sheet.
  2. Mini‑lecture (10 '): Review one‑one definition, introduce the four‑step procedure, and demonstrate with $f(x)=3x+2$ using the projector.
  3. Guided Practice (12 '): Work through the quadratic example $f(x)=x^{2}$ (domain $x\ge0$) together, emphasizing domain restriction.
  4. Partner Activity (15 '): Students solve three practice problems from the worksheet, checking each other’s work with the checklist.
  5. Formative Check (5 '): Quick exit quiz – write the inverse of $g(x)=\frac{2}{x}$ and state its domain.
  6. Reflection (3 '): Whole‑class discussion of common mistakes and how to avoid them.
Conclusion:
Recap the key steps: write $y=f(x)$, swap variables, solve for $y$, and record domain/range. Students complete an exit ticket by writing one correct inverse and one common error to watch for. Assign homework: three additional inverse problems, including a non‑linear function that requires domain restriction.