Class 11 Maths - MAHARASHTRA
Relations and Functions
The 'Relations and Functions' chapter in Class 11 Mathematics lays the foundation for advanced algebra and calculus. Students learn to map elements between sets using Cartesian products, understand ordered pairs, and differentiate between general relations and specific functions. Mastering domain, co-domain, and range is crucial. For MSBSHSE board exams, this chapter is high-scoring and bridges basic algebra with higher-level mathematical thinking, frequently appearing in both short and long-answer sections.
Start Learning FreeKey Concepts
Cartesian Product of Sets
The set of all possible ordered pairs (a, b) where a belongs to set A and b belongs to set B, denoted as A × B.
Relation
A subset of the Cartesian product A × B, establishing a specific connection or rule between elements of two sets.
Function
A special type of relation where every element in the domain is associated with a unique element in the co-domain.
Domain, Co-domain, and Range
Domain is the set of all possible inputs, co-domain is the target set, and range is the set of all actual outputs of a function.
Types of Functions
Classification of functions such as one-one (injective), onto (surjective), bijective, constant, identity, and polynomial functions.
Important Formulas
Board Exam Info
In the Maharashtra (MSBSHSE) Class 11 Mathematics examination, this chapter typically carries around 4 to 6 marks. Common question types include finding the domain and range of given functions, determining whether a relation is a function, finding Cartesian products, and solving algebraic operations on functions.
Frequently Asked Questions
What is the difference between a relation and a function?
Every function is a relation, but not every relation is a function. In a function, every input has one and only one output, whereas a relation can map one input to multiple outputs.
How do I find the domain of a rational function?
To find the domain of a rational function, set the denominator equal to zero and exclude those real values from the set of all real numbers where the denominator becomes zero.
Is the Cartesian product commutative?
No, A × B is generally not equal to B × A unless set A equals set B or one of the sets is empty.
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