Mathematics Advanced Year 11 - Module 1 - Lesson 6

Inverse Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Every time you unlock your phone with a passcode, encryption turns your code into something unreadable — and only the inverse process can turn it back. That is the power of an inverse function: it undoes what the original function did, perfectly and predictably.

  • The definition of an inverse function
  • Why an inverse swaps the domain and range

2. Success Criteria

By the end, you should be able to:

  • The definition of an inverse function
  • The algebraic method for finding an inverse
  • That $f(f^{-1}(x)) = x$

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The definition of an inverse function". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The algebraic method for finding an inverse". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Inverse Functions: "That $f(f^{-1}(x)) = x$".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Inverse Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Inverse Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Inverse Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The definition of an inverse function

Band 32 marks
Success criterion 2

Prove that you can: The algebraic method for finding an inverse

Band 43 marks
Success criterion 3

Prove that you can: That $f(f^{-1}(x)) = x$

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 6

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Mathematics Advanced Year 11 - Module 1 - Lesson 6

Inverse Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Every time you unlock your phone with a passcode, encryption turns your code into something unreadable — and only the inverse process can turn it back. That is the power of an inverse function: it undoes what the original function did, perfectly and predictably.

  • The definition of an inverse function
  • Why an inverse swaps the domain and range

2. Success Criteria

By the end, you should be able to:

  • The definition of an inverse function
  • The algebraic method for finding an inverse
  • That $f(f^{-1}(x)) = x$

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The definition of an inverse function". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The algebraic method for finding an inverse". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Inverse Functions: "That $f(f^{-1}(x)) = x$".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Inverse Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Inverse Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Inverse Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The definition of an inverse function

Band 32 marks
Success criterion 2

Prove that you can: The algebraic method for finding an inverse

Band 43 marks
Success criterion 3

Prove that you can: That $f(f^{-1}(x)) = x$

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 6

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Mathematics Advanced Year 11 - Module 1 - Lesson 6

Inverse Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

Every time you unlock your phone with a passcode, encryption turns your code into something unreadable — and only the inverse process can turn it back. That is the power of an inverse function: it undoes what the original function did, perfectly and predictably.

  • The definition of an inverse function
  • Why an inverse swaps the domain and range

2. Success Criteria

By the end, you should be able to:

  • The definition of an inverse function
  • The algebraic method for finding an inverse
  • That $f(f^{-1}(x)) = x$

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "The definition of an inverse function". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "The algebraic method for finding an inverse". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Inverse Functions: "That $f(f^{-1}(x)) = x$".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Inverse Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Inverse Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Inverse Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: The definition of an inverse function

Band 32 marks
Success criterion 2

Prove that you can: The algebraic method for finding an inverse

Band 43 marks
Success criterion 3

Prove that you can: That $f(f^{-1}(x)) = x$

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 6