Function — Chapter Summary
Gujarat Board · Class 11 · Statistics
Summary of Function for Gujarat Board Class 11 Statistics. Key concepts: A function from set A, For function f and Functions are denoted as f.
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Overview
Functions form the foundation of mathematical relationships between two sets. In our daily life, we encounter many situations where one quantity depends on another - like the cost of items depending on their quantity, or marks obtained depending on study hours. A function is a special type of relati
Key Concepts
A function from set A
A function from set A to set B is a rule that assigns to each element of A exactly one element of B. Mathematically, if f: A → B, then for every x ∈ A
For function f
For function f: A → B: Domain (Df) = set A (input values), Codomain = set B (possible output values), Range (Rf) = {f(x) | x ∈ A} (actual output value
Functions are denoted as f
Functions are denoted as f: A → B, read as 'f maps A to B'. The value of function f at x is written as f(x). Step-by-step notation: (1) Write f: follo
A function f
A function f: A → B is one-one if different elements in domain have different images in codomain. Mathematically: if x₁ ≠ x₂, then f(x₁) ≠ f(x₂). Test
A function f
A function f: A → B is many-one if at least two different elements in domain have the same image in codomain. Test: if x₁ ≠ x₂ but f(x₁) = f(x₂), then
Learning Objectives
- Understand the definition and concept of a function as a special relation between two sets
- Identify and distinguish between domain, codomain, and range of a function
- Learn proper mathematical notation for representing functions
- Classify functions into different types: one-one, many-one, and constant functions
- Determine when two functions are equal and understand the conditions required
Frequently Asked Questions
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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