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  • Please solve rd sharma class 12 chapter Functions exercise 2.4  question 2 sub-question (ii) maths textbook solution.

Please solve rd sharma class 12 chapter Functions exercise 2.4  question 2 sub-question (ii) maths textbook solution.

Answers (1)

Answer:

f^{-1} doesn't exist.

Given:

A=\left \{ 1,3,5,7,9 \right \},\: B=\left \{ 0,1,9,25,49,81 \right \},f\left ( x \right )=x^{2}

Solution: 

Let us check one-one

f\left ( x \right )=x^{2},f\left ( 1 \right )=1,f\left ( 3 \right )=3^{2}=9,f\left ( 5 \right )=5^{2}=25,f\left ( 7 \right )=7^{2}=49,f\left ( 9 \right )=9^{2}=81

\therefore f=\left \{ \left ( 1,1 \right ),\left ( 3,9 \right ),\left ( 5,25 \right ),\left ( 7,49 \right ),\left ( 9,81 \right ) \right \}

The different elements of the domain have different images in the codomain.

Thus, f is one-one.

This is not onto because the element 0 in the codomain \left ( B \right ) has no preimage in the domain \left ( A \right ).

Therefore, f^{-1} doesn't exist.

 

Posted by

Gurleen Kaur

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