Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
To prove one-one & onto (injective, surjective, bijective)
Onto function
One One and Onto functions (Bijective functions)
Example 7
Example 8 Important
Example 9
Example 11 Important
Misc 2
Ex 1.2, 5 Important
Ex 1.2 , 6 Important
Example 10
Ex 1.2, 1
Ex 1.2, 12 (MCQ)
Ex 1.2, 2 (i) Important
Ex 1.2, 7 (i)
Ex 1.2 , 11 (MCQ) Important
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3
Ex 1.2 , 4
Example 25
Example 26 Important
Ex 1.2 , 10 Important
Misc 1 Important
Example 13 Important You are here
Example 14 Important
Ex 1.2 , 8 Important
Example 22 Important
Misc 4 Important
To prove one-one & onto (injective, surjective, bijective)
Last updated at June 6, 2023 by Teachoo
Example 13 (Method 1) Show that an onto function f : {1, 2, 3} → {1, 2, 3} is always one-one. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Following cases are possible Since every element 1,2,3 has either of image 1,2,3 and that image is unique f is one-one Since every element 1, 2, 3 has either of image 1, 2, 3 and that image is unique ∴ f is one-one Example 13 (Method 2) Show that an onto function f : {1, 2, 3} → {1, 2, 3} is always one-one. Suppose f is not one-one, So, atleast two elements will have the same image If 1 & 2 have same image 1, & 3 has image 3 Then, 2 has no pre-image, Hence, f is not onto. But, given that f is onto, So, f must be one-one