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  • Need solution for rd sharma maths class 12 chapter functions exercise 2.4 question 1 sub-question (iii)

Need solution for rd sharma maths class 12 chapter functions exercise 2.4 question 1 sub-question (iii)

Answers (1)

Answer:

Yes, h is a bijection.

Given:

h:\left \{ 2,3,4,5 \right \}\rightarrow \left \{ 7,9,11,13\right \}\: with\: h=\left \{ \left ( 2,7 \right ),\left ( 3,9 \right ),\left ( 4,11 \right ),\left ( 5,13 \right ) \right \}

Hint:

A function has an inverse if it is one-one and onto.

Solution:

Let us check one-one

h=\left \{ \left ( 2,7 \right ),\left ( 3,9 \right ),\left ( 4,11 \right ),\left ( 5,13 \right ) \right \}

 

Since all element has unique image h is one-one.

Check onto,

Since each and every image there is a corresponding element.

\therefore h is onto.

Since the function is both one-one and onto, it will have an inverse.

h=\left \{ \left ( 2,7 \right ),\left ( 3,9 \right ),\left ( 4,11 \right ),\left ( 5,13 \right ) \right \}

h^{-1}=\left \{ \left ( 7,2 \right ),\left ( 9,3 \right ),\left ( 11,4 \right ),\left ( 13,5 \right ) \right \}

Posted by

Gurleen Kaur

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