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Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1  question 15

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            f:A\rightarrow A , given byA=\left \{ 1,2,3 \right \}.

To prove:

Onto function must be one-one.


Let f is not one-one then there exists two elements say 1 and 2 in the domain having same image  in the co-domain.

Also, the image of 3 under f can be only one element.

\therefore The range set will have at most two element of the co-domain, but we know that in the range set we have three elements \left \{ 1,2,3 \right \}.

i.e.  There arises a contradiction that f  is not onto function.

Hence f must be one-one.

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