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

$f(x)=y$

Given:

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

Hint:

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.$f(x_1)=f(x_2)$, then$x_1=x_2$

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.

Solution:

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

Let the function$f:N \rightarrow N$, given by$f(1)=f(2)=1$

Here,   $f(x)=f(2)=1$

$f(x)=f(1)=1$

Since different elements $1,2$  have same image 1,

$\therefore f$ is not one-one.

Let$f(x)=y$, 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 by$f(1)=f(2)=1$ is not one-one but onto.