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Inverse Functions
A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
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Inverse Functions
What is it?
A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
In simple words
- A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
- Worked pattern: For f(x)=3x-6, f-1(x)=x+63.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Inverse functions: A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
What you should learn
- State the rule for inverse functions.
- Solve a inverse functions problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
CONCEPT AND RULE
A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
METHOD
For inverse functions, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For f(x)=3x-6, f-1(x)=x+63.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve inverse functions
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Inverse functions
- rule
- worked example
- worked example
How the ideas connect
Worked example: For f(x)=3x-6, f-1(x)=x+63.
Deeper understanding
Go beyond memorising Inverse Functions. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: For f(x)=3x-6, f-1(x)=x+63.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Inverse functions
- rule
- worked example
- Inverse functions: A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
- CONCEPT AND RULE: A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
- METHOD: For inverse functions, identify the given information and required result. Select the matching defin
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Inverse Functions: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Inverse functions
- rule
- worked example
- Inverse functions: A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
Important formulas
- Inverse functions
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Inverse functions
rule
worked example
Inverse functions: A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
- Definition
- A one-one function has an inverse found by writing y=f(x), interchanging x and y, and solving for y.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Inverse Functions.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Inverse Functions and say why it fits.
Mistake
Q4. State one common mistake students make about Inverse Functions.
Exam note
Q5. Write a short exam note on Inverse Functions: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.