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Types of Functions
Example Exercise
Example exercise
Example Exercise
Example Exercise
Example Exercise
Example Exercise
Example Exercise
Example Exercise
Exercise
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11

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NCERT XII
Chapter 1: Relations and Functions
Section 1.3: Functions

Section 1.3: Functions

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Example Exercise

Example 13
Show that an onto function \(f : \{1, 2, 3\} \to \{1, 2, 3\}\) is always one-one.

Solution
Suppose \(f\) is not one-one. Then there exists two elements, say 1 and 2 in the domain whose image in the co-domain is same.
Also, the image of 3 under \(f\) can be only one element.
Therefore, the range set can have at the most two elements of the co-domain \(\{1, 2, 3\}\),
showing that \(f\) is not onto, a contradiction.
Hence, \(f\) must be one-one.

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