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Misc 11 - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at Aug. 11, 2021 by Teachoo
Finding Inverse
Identity Function
Inverse of a function
How to check if function has inverse?
Example 22
Ex 1.3, 5 (i)
How to find Inverse?
Example 28 (a)
Misc 11 (i) Important You are here
Ex 1.3, 11
Example 27 Important
Misc 1
Ex 1.3 , 6
Ex 1.3, 14 (MCQ) Important
Example 23 Important
Misc 2
Ex 1.3 , 4
Example 24
Ex 1.3 , 8 Important
Example 25 Important
Ex 1.3 , 9 Important
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
- Composite functions and one-one onto
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Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Misc 11 Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists. (i) F = {(a, 3), (b, 2), (c, 1)} A function has inverse if it is one-one and onto Check one one F = {(a, 3), (b, 2), (c, 1)} Since each element has unique image, F is one-one Check onto Since for every image, there is a corresponding element, ∴ F is onto. Since function is both one-one and onto it will have inverse F = {(a, 3), (b, 2), (c, 1)} F−1 = {(3, a), (2, b), (1, c)}.
