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Last updated at Jan. 28, 2020 by Teachoo

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Ex 1.3, 3 Find ๐๐๐ and ๐๐๐, if (i) f(x) = |๐ฅ| and g (x) = |5๐ฅ โ2| f(x) = |๐ฅ| , g(x) = |5๐ฅโ2| f(x) = |๐ฅ| f(g(x)) = |๐(๐ฅ)| fog(x) = |(|5๐ฅ โ2|)| = |๐๐ โ๐| g(x) = |5๐ฅ โ2| g(f(x)) =|5๐(๐ฅ) โ2| gof (x) = |(๐|๐|โ๐)| Ex 1.3, 3 Find ๐๐๐ and ๐๐๐, if (ii) f (x) =8๐ฅ3 and g (x) = ๐ฅ^(1/3) f(x) = 8x3 g(x) = ๐ฅ^(1/3) f(x) = 8x3 f(g(x)) = 8 g(x)3 fog(x) = ใ"8" ใ(๐ฅใ^(1/3))ใ^3 = 8 ๐ฅ^(1/3 ร 3) = 8x g(x) =๐ฅ^(1/3) g(f(x)) = ใ๐(๐ฅ)ใ^(1/3) gof (x) = ใ"(8" ๐ฅ3)ใ^(1/3) = ((2๐ฅ)^3 )^(1/3) = ใ"(2x" )ใ^(3 ร 1/3) = 2x

Composite functions

Composition of functions

Example 15 Not in Syllabus - CBSE Exams 2021

Ex 1.3, 1 Not in Syllabus - CBSE Exams 2021

Example 16 Not in Syllabus - CBSE Exams 2021

Ex 1.3, 3 Important Not in Syllabus - CBSE Exams 2021 You are here

Ex 1.3 , 13 Important Not in Syllabus - CBSE Exams 2021

Misc 3 Important Not in Syllabus - CBSE Exams 2021

Example 17 Not in Syllabus - CBSE Exams 2021

Example 26 Not in Syllabus - CBSE Exams 2021

Misc 18

Ex 1.3, 2 Not in Syllabus - CBSE Exams 2021

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
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.