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Question 4 - Composite functions and one-one onto - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Composite functions and one-one onto
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
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Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Question 4 Consider functions f and g such that composite gof is defined and is one-one. Are f and g both necessarily one-one. Here, we take examples and function f, g And draw their set using arrow diagram Here, f is one-one But g is not one And finding gof using arrow diagram, we see that gof is one-one But g & f are not necessarily one-one
