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

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

Answers (1)

    

f_2 is one-one and onto function.

Given:

            f_{2}=\{(2, a),(3, b),(4, c)\} ; A=\{2,3,4\} ; B=\{a, b, c\}

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:

          \begin{aligned} &f_{2}(2)=a \\ &f_{2}(3)=b \\ &f_{2}(4)=c \end{aligned}

Every element of A has different images in B.

\therefore Function f_2 is one-one.

Surjectivity:

Co-domain of f_2=\left \{ a,b,c \right \}

            Range of f_2= set of image\left \{ a,b,c \right \}

            Codomain = Range

So, f_2 is onto.

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