#### Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1 question 2 sub question (iii)

$f_3$ is not one-one and onto function.

Given:

$f_{3}=\{(a, x),(b, x),(c, z),(d, z)\} ; A=\{a, b, c, d\} ; B=\{x, y, z\}$

Hint:

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

Onto function means every element in the codomain has at least one pre image in the domain of function.

Solution:

We need to find the one-one function

Injectivity: (one-one)

\begin{aligned} &f_{3}(a)=x, f_{3}(c)=z \\ &f_{3}(b)=x, f_{3}(d)=z \end{aligned}

Here $f_3(a),f_3(b)$ have the same image x

Also $f_3(c),f_3(d)$ have the same image z

Therefore,$f_3$ is not one-one.

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