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5.Functions – Concept & Notation
Class 11 • Mathematics • NCERT
Functions – Concept & Notation
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This lesson introduces the concept of a function as defined in NCERT Class 11. Students learn how a function maps elements from one set to another and understand standard function notation with simple examples.
Lesson Objectives
- Understand the concept of a function.
- Differentiate between relation and function.
- Learn standard function notation.
- Identify domain, codomain, and range.
1. What Is a Function?
A function is a relation in which every element of the first set is related to exactly one element of the second set.
Key idea (NCERT):
• Every input has one and only one output
• Every input has one and only one output
2. Function as a Mapping
A function can be viewed as a mapping from one set to another.
If f maps A to B, then we write:
f : A → B
f : A → B
3. Function Notation
If f is a function from A to B and x ∈ A, then the image of x under f is written as f(x).
Example:
If f(x) = x², then f(2) = 4
If f(x) = x², then f(2) = 4
4. Domain, Codomain, and Range (Intro)
Every function has three important parts.
• Domain: Set of all inputs
• Codomain: Set in which outputs lie
• Range: Actual outputs obtained
• Codomain: Set in which outputs lie
• Range: Actual outputs obtained
Practice Questions (NCERT)
- What is a function?
- Can a function assign two outputs to one input?
- Write the notation for a function from A to B.
- What does f(x) represent?
- Is every relation a function?
- Name the three parts of a function.
- If f(x) = x + 1, find f(3).
- What is the domain of a function?
- What is the range of a function?
- Is a function a special type of relation?
✅ Show Answer Key
- A relation with exactly one output for each input.
- No.
- f : A → B
- Image of x under f.
- No.
- Domain, codomain, range.
- 4
- Set of all inputs.
- Set of actual outputs.
- Yes.
© Aviate Learning – Relations & Functions (NCERT Class 11)