# Ex 1.3 , 14 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 17, 2018 by Teachoo

Last updated at Dec. 17, 2018 by Teachoo

Transcript

Ex 1.3 , 14 Let f : R โ {(โ4)/3} โ R be a function defined as . f (x) = 4๐ฅ/(3๐ฅ + 4) The inverse of f is map g: Range f โ R โ {(โ4)/3}given by (A) g (y) = 3๐ฆ/(3โ4๐ฆ) (B) g (y) = 4๐ฆ/(4โ3๐ฆ) (C) g (y) = 4๐ฆ/(3โ4๐ฆ) (D) g (y) = 3๐ฆ/(4โ3๐ฆ) f(x) = 4๐ฅ/(3๐ฅ + 4) Calculating inverse Take f(x) = y Hence, equation becomes y = 4๐ฅ/(3๐ฅ + 4) y(3x + 4) = 4x 3xy + 4y = 4x 3xy โ 4x = โ 4y x(3y โ 4) = โ 4y x = (โ4๐ฆ)/(3๐ฆ โ 4) x = (โ4๐ฆ)/(โ1(โ3๐ฆ + 4)) x = 4๐ฆ/((4 โ 3๐ฆ)) So, inverse of f = 4๐ฆ/((4 โ 3๐ฆ)) โ g(y) = 4๐ฆ/((4 โ 3๐ฆ)) Hence, B is the correct answer

Finding Inverse

Identity Function

Inverse of a function

How to check if function has inverse?

Example 22

Ex 1.3, 5

How to find Inverse?

Example 28 Important

Misc 11

Ex 1.3, 11 Important

Example 27

Example 23 Important

Misc 1

Ex 1.3 , 6 Important

Ex 1.3 , 14 Important You are here

Misc 2

Ex 1.3 , 4

Example 24

Ex 1.3 , 8

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
- 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.