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Onto and Into Mappings
A function is onto when every codomain element is an output; range must equal codomain.
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Onto and Into Mappings
What is it?
A function is onto when every codomain element is an output; range must equal codomain.
In simple words
- A function is onto when every codomain element is an output; range must equal codomain.
- Worked pattern: f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Onto and into mappings: A function is onto when every codomain element is an output; range must equal codomain.
What you should learn
- State the rule for onto and into mappings.
- Solve a onto and into mappings problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
A function is onto when every codomain element is an output; range must equal codomain.
CONCEPT AND RULE
A function is onto when every codomain element is an output; range must equal codomain.
METHOD
For onto and into mappings, 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
f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
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 onto and into mappings
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
- Onto and into mappings
- rule
- worked example
- worked example
How the ideas connect
Worked example: f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
Deeper understanding
Go beyond memorising Onto and Into Mappings. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Onto and into mappings
- rule
- worked example
- Onto and into mappings: A function is onto when every codomain element is an output; range must equal codomain.
- CONCEPT AND RULE: A function is onto when every codomain element is an output; range must equal codomain.
- METHOD: For onto and into mappings, identify the given information and required result. Select the matching
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 Onto and Into Mappings: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Onto and into mappings
- rule
- worked example
- Onto and into mappings: A function is onto when every codomain element is an output; range must equal codomain.
Important formulas
- Onto and into mappings
- 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.
Onto and into mappings
rule
worked example
Onto and into mappings: A function is onto when every codomain element is an output; range must equal codomain.
A function is onto when every codomain element is an output; range must equal codomain.
- Definition
- A function is onto when every codomain element is an output; range must equal codomain.
- 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 Onto and Into Mappings.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Onto and Into Mappings and say why it fits.
Mistake
Q4. State one common mistake students make about Onto and Into Mappings.
Exam note
Q5. Write a short exam note on Onto and Into Mappings: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.