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6.Types of Functions
Class 11 • Mathematics • NCERT
Types of Functions
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This lesson explains different types of functions strictly as per NCERT Class 11. Students learn one–one, many–one, onto, and into functions using simple definitions and examples required for board examinations.
Lesson Objectives
- Understand different types of functions.
- Identify one–one and many–one functions.
- Differentiate between onto and into functions.
- Solve NCERT-style questions confidently.
1. One–One (Injective) Function
A function is called one–one if different elements of the domain have different images.
If f(a₁) = f(a₂), then a₁ = a₂
2. Many–One Function
A function is called many–one if two or more different elements of the domain have the same image.
Example:
f(x) = x² is many–one because f(2) = f(–2)
f(x) = x² is many–one because f(2) = f(–2)
3. Onto (Surjective) Function
A function f : A → B is called onto if every element of B has at least one pre-image in A.
Range = Codomain
4. Into Function
A function f : A → B is called into if there exists at least one element in B which has no pre-image in A.
Range ⊂ Codomain
5. Important NCERT Notes
• A function can be one–one and onto
• A function can be many–one and onto
• A one–one function may or may not be onto
• A function can be many–one and onto
• A one–one function may or may not be onto
Practice Questions (NCERT)
- Define a one–one function.
- Define a many–one function.
- What is an onto function?
- What is an into function?
- Can a function be both one–one and onto?
- Is f(x) = x² one–one?
- Is f(x) = x³ one–one?
- What is the relation between range and codomain in an onto function?
- What is the relation between range and codomain in an into function?
- Are these definitions strictly from NCERT?
✅ Show Answer Key
- Different inputs give different outputs.
- Different inputs give the same output.
- Every element of codomain has a pre-image.
- Some elements of codomain have no pre-image.
- Yes.
- No.
- Yes.
- Range = Codomain.
- Range ⊂ Codomain.
- Yes.
© Aviate Learning – Relations & Functions (NCERT Class 11)