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Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 1 sub question (ii)  maths textbook solution.

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The example for a function which is not one-one but onto.


One-one function means every element in the domain has a distinct image in the co-domain. If one-one is given for any function.f(x_1)=f(x_2), thenx_1=x_2

Where, x_1,x_2 \in domain of f(x)

Onto function defined as every element in the co-domain has at least one  pre image in the domain of function.


Here, we need to give an example of a function for a not one-one but onto function.

Let the functionf:N \rightarrow N, given byf(1)=f(2)=1

Here,   f(x)=f(2)=1


Since different elements 1,2  have same image 1,

\therefore f is not one-one.

Letf(x)=y, such that y\in N

Here,y is a natural number and for every y there is a value of x which is a natural number.

Hence,f is onto.

So, the function f:N \rightarrow N, given byf(1)=f(2)=1 is not one-one but onto.

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