MathematicsChapter 1: Functions and Graphs
Onto and Into Mappings
A function is onto when every codomain element is an output; range must equal codomain.
Learning objectives
- 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.
Definition
A function is onto when every codomain element is an output; range must equal codomain.
Formula
x=cuberoot(y) exists for every real y.
Where / symbols
- 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 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
- 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.
Worked example
- Worked example:
- f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Onto and into mappings
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Onto and Into Mappings
Sticky Notes · Formula and Worked Revision
Core Idea
- A function is onto when every codomain element is an output; range must equal codomain.
Rule / Formula
- A function is onto when every codomain element is an output; range must equal codomain.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- f:R->R, f(x)=x^3 is onto because x=cuberoot(y) exists for every real y.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- 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.
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