

Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Ex 1.2 , 3 (Introduction) Prove that the Greatest Integer Function f: R R given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x. f(x) = [x] = greatest integer less than equal to x Example: [1] = 1 [1.01] = 1 [1.2] = 1 [1.9] = 1 [1.99] = 1 [2] = 2 Ex 1.2 , 3 Prove that the Greatest Integer Function f: R R given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x. f(x) = [x] where [x] denotes the greatest integer less than equal to x Check one-one f(x) = [x] Eg: f(1) = [1] = 1, f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1, f(1.99) = [1.99] = 1, Check onto f(x) = [x] Let y = f(x) y = [x] i.e. y = Greatest integer less than or equal to x Hence, value of y will always come an integer. But y is a real number Hence f is not onto.
To prove one-one & onto (injective, surjective, bijective)
Onto function
One One and Onto functions (Bijective functions)
Example 7
Example 8
Example 9
Example 11 Important
Misc 5
Ex 1.2, 5 Important
Ex 1.2 , 6
Example 10
Ex 1.2, 1
Ex 1.2, 12
Ex 1.2 , 2 Important
Ex 1.2 , 7
Ex 1.2 , 11
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3 You are here
Ex 1.2 , 4
Example 50
Example 51 Important
Ex 1.2 , 10 Important
Misc. 4 Important
Example 13 Important
Example 14 Important
Ex 1.2 , 8 Important
Example 46 Important
Misc 10 Important
About the Author