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Grade 11 Math Lab: Transcendence & Limits FREE
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Inverse Functions
Learning Objectives
- Find inverse functions
- Verify inverse relationships
- Graph inverses
Key Concepts
Inverse Function
f⁻¹(x) undoes f(x): f(f⁻¹(x)) = x
One-to-One
Each output has exactly one input (passes horizontal line test)
Theory
**To find f⁻¹(x):**
1. Replace f(x) with y
2. Swap x and y
3. Solve for y
**Graph:** Reflect f(x) across y = x line.
**Verification:** f(f⁻¹(x)) = x and f⁻¹(f(x)) = x
**Note:** Only one-to-one functions have inverses. Restrict domain if needed.
Examples
Find inverse of f(x) = 2x + 3
Solution: y = 2x+3 → x = 2y+3 → y = (x-3)/2. f⁻¹(x) = (x-3)/2