Stage A • Mission Brief & Authentic Dilemma

Subtopic 1.3: Inverse Functions (Fungsi Songsang)

KSSM Additional Mathematics Form 4 — Textbook pp. 20–30

Authentic Real-World Challenge

The New York Weather Dilemma: Inverting Temperature Conversions

You read news online that the temperature in New York is 39°F. You need to calculate the exact temperature in degrees Celsius (°C).

The standard thermometer relation is F(C) = 95C + 32.

⇒ Rather than re-solving an algebraic equation every single day, we build the Inverse Function:
C(F) = 59(F − 32)!

For 39°F: C(39) = 59(39 − 32) = 359 ≈ 3.89°C!

🎯 Malaysian KSSM DSKP Learning Standards:

  • 1.3.1: Describe the inverse of a function (f−1(x) ≠ 1f(x)).
  • 1.3.2: Make and verify conjectures on properties of inverse functions (One-to-one, Horizontal Line Test, ff−1(x) = x, reflection across y = x).
  • 1.3.3: Determine inverse functions algebraically in 3 systematic steps.

👤 Student Identification

Stage B • Digital Manipulative Discovery Lab

Visualizing the 5 Core Properties of Inverse Functions

Manipulate inputs, scan with horizontal lines, and inspect reflection across identity line y = x.

Forward Machine f(x) f(x) = 2x + 3 y = f(x) Inverse Machine f⁻¹(y) f⁻¹(y) = (y − 3) ÷ 2 x = f⁻¹(y) 7 2

⚙️ Machine Gearbox Controls

Input Object x: 2
x y

📊 Choose Function to Test:

Scan Horizontal Line y: 1
x y 0 −6 3 4 10 −6 3 4 10 Line y = x

📖 Select Textbook Reflection Model:

Move Object $a$ along Domain of $f$: 3
Stage C • Interactive Worked Examples

Step-by-Step Textbook Mastery (TB pp. 21–28)

Complete intermediate steps and verify inverse relations with immediate feedback.

Stage D • Scaffolded Guided Practice

Textbook Exercise Drills with Multi-Tier Hints

Self Practice 1.8, 1.9 & 1.10 — Instant remediation for common exam pitfalls.

Stage E • Independent Challenge

Tiered SPM Examination Problems

Foundation, Intermediate & Advanced KBAT Applications.

Stage F • Diagnostic Exit Ticket

3-Question Diagnostic & Learning Report

Verify your mastery of Inverse Functions and generate your official completion certificate.