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

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


One-one function means every element in the domain has a distinct image in the co-domain

.f(x_1)=f(x_2), thenx_1=x_2

Where, X_1,X_2 domain off(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 one-one but not onto.

Let we consider the function,

f:N \rightarrow N, given byf(x)=2N

Let us consider two elementsx_1 and x_2 in the domain of f, so we get


Now we know the condition for finding a one-one function.

            2x_1= 2x_2

            x_1= x_2

            Hence, the function is one-one.

Now, we need to provef(x)=2xis not onto

Let f(x)=y, such that  x,y\in N

We get,



If we put y=1,

            x=\frac{1}{2}=0.5, which is cannot be true as x \in N supposed in solution.

Hence, the given function is not onto.

So, f(x)=2x is an example of one-one but not onto function.

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