# Example 13 - Chapter 2 Class 11 Relations and Functions

Last updated at Dec. 4, 2018 by Teachoo

Last updated at Dec. 4, 2018 by Teachoo

Transcript

Example 13, Define the function f: R → R by y = f(x) = x2, x ∈ R. Complete the table given below by using this definition. What is the domain and range of this function? Draw the graph of f. Given f(x) = x2 We have to find f(-4) To find f( – 4), we put x = – 4 in f(x) f(x) = ( – 4)2 = 16 f(x) = ( –3)2 = 9 f(x) = ( – 2)2 = 4 f(x) = ( – 1)2 = 1 f(x) = (0)2 = 0 f(x) = (1)2 = 1 f(x) = (2)2 = 4 f(x) = (3)2 = 9 f(x) = (4)2 = 16 Here we are given x is real & we can put any value of x Hence, Domain = All possible value of x = R We note that f(x) has a minimum value of 0 and the value can increase up to infinity. So, Range of f = All possible values of f(x) = [0, ∞ ) To find f(-1.5), we put x = – 1.5 f(x) = 1/(−1.5) = −10/15 = −2/3 = – 0.66 To find f( – 1), we put x = – 1 f(x) = 1/(−1) = −1 To find f( – 0.5), we put x = – 0.5 f(x) = 1/(−0.5) = −10/5 = – 2 To find f(0.25), we put x = 0.25 f(x) = 1/0.25 = 100/25 = 4 To find f(0.5), we put x = 0.5 f(x) = 1/0.5 = 10/5 = 2 To find f(1), we put x = 1 f(x) = 1/1 = 1 To find f(1.5), we put x = 1.5 f(x) = 1/1.5 = 10/15 = 2/3 = 0.66 To find f(2), we put x = 2 f(x) = 1/2 = 0.5 Given f(x) = 1/𝑥 , x ∈ R – {0} Hence, x & y can be any real number except 0 Domain = All possible values of x = R – {0} Range = All possible values of f(x) or y = R – {0}

Finding Domain and Range - By drawing graphs

Chapter 2 Class 11 Relations and Functions

Concept wise

- Finding Cartesian Product
- Equality of 2 ordered pairs
- Number of elements
- Operations on sets+ cartesian product
- Relations - Definition
- Finding Relation - Set-builder form given
- Finding Relation - Arrow Depiction given
- Number of Relations
- Functions - Definition
- Finding values at certain points
- Different Functions and their graphs
- Finding Domain and Range - By drawing graphs
- Finding Domain and Range - General Method
- Algebra of real functions

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.