# Example 13 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Jan. 28, 2020 by Teachoo

Last updated at Jan. 28, 2020 by Teachoo

Transcript

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

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Chapter 1 Class 12 Relation and Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.