# Misc 3 - Chapter 1 Class 12 Relation and Functions

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Misc 3 If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)). f(x) = x2 − 3x + 2. f(f(x)) = f(x)2 − 3f(x) + 2. = (x2 – 3x + 2)2 – 3(x2 – 3x + 2) + 2 = (x2)2 + (3x)2 + 22 – 2x2 (3x) + 2x2(2) – 2x2(3x) – 3(x2 – 3x + 2) + 2 = x4 + 9x2 + 4 – 6x3 – 12x + 4x2 – 3x2 + 9x – 6 + 2 = x4 – 6x3 + 9x2 + 4x2 – 3x2 – 12x + 9x – 6 + 2 + 4 = x4 – 6x3 + 10x2 – 3x

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.