# Get Answers to all your Questions

#### Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 2 sub question (i)  maths textbook solution.

$f_1$ is one-one and onto function.

Given:

$f_{1}=\{(1,3),(2,5),(3,7)\} ; A=\{1,2,3\} ; B=\{3,5,7\}$

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_{1}(1)=3 \\ &f_{1}(2)=5 \\ &f_{1}(3)=7 \end{aligned}

Every element of A has different images in B.

$\therefore$ Function $f_1$ is one-one.

Surjectivity: (onto)

Co-domain of$f_1= \left \{ 3,5,7 \right \}$

Range of $f_1$ set of image$\left \{ 3,5,7 \right \}$

Co-domain=Range

So, $f_1$ is onto.