# Misc. 4

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc. 4 Show that function f: R {x R: 1 < x < 1} defined by f(x) = x 1 + , x R is one-one and onto function. f: R {x R: 1 < x < 1} f(x) = x 1 + We know = , 0 , <0 So, = 1 + , 0 & 1 , <0 Checking one-one Hence, if f(x1) = f(x2) , then x1 = x2 f is one-one = 1 + , 0 & 1 , <0 Checking onto Thus, x = 1 , for x 0 & x = 1 + , for x < 0 Here, y {x R: 1 < x < 1} i.e. Value of y is from 1 to 1 , 1 < y < 1 If y = 1, x = 1 will be not defined, But here 1 < y < 1 So, x is defined for all values of y. & x R f is onto Hence, f is one-one and onto.

Chapter 1 Class 12 Relation and Functions

Ex 1.2, 5
Important

Ex 1.2 , 10 Important

Example 23 Important

Example 25 Important

Ex 1.3, 3 Important

Ex 1.3 , 6 Important

Ex 1.3 , 8 Important

Ex 1.3 , 9 Important

Ex 1.3 , 13 Important

Ex 1.3 , 14 Important

Ex 1.4, 11 Important

Misc 3 Important

Misc. 4 Important You are here

Misc 14 Important

Misc 18 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.