Maths Extension 1 Year 11 - Module 1 - Lesson 7
Graphs of Inverse Functions
Name
Date
Class
1. Lesson focus
Graphs of inverse functions. The graph of f⁻¹ is the reflection of f in y=x; coordinates swap, as do the domain and range.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. A point (2,5) lies on y=f(x). What corresponding point lies on y=f⁻¹(x)?
3. For f(x)=x² restricted to x≥0, give the inverse graph equation and its domain.
3. Challenge
Reflect the point (−1,1) on y=x². Does the reflected point lie on the inverse of x² restricted to x≥0?
4. Multiple choice
The inverse graph is obtained by reflecting in which line?
A. y=0
B. y=x
C. x=0
D. y=−x
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Find the inverse of f(x)=3x−6.
y=3x−6 ⇒ x=(y+6)/3; f⁻¹(x)=(x+6)/3.
2. A point (2,5) lies on y=f(x). What corresponding point lies on y=f⁻¹(x)?
Swap coordinates: (5,2).
3. For f(x)=x² restricted to x≥0, give the inverse graph equation and its domain.
y=√x, domain x≥0; it is the reflection of y=x² across y=x.
Challenge. Reflect the point (−1,1) on y=x². Does the reflected point lie on the inverse of x² restricted to x≥0?
It reflects to (1,−1), which is not on y=√x; the point (−1,1) was outside the restricted original domain.
Multiple choice. The inverse graph is obtained by reflecting in which line?
Correct answer: B. Swapping every input-output pair reflects the graph across the line y=x.
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