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  • Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 7 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 7 Maths Textbook Solution.

Answers (1)

Answer:              

f^{-1}\left ( x \right )=\sqrt{x-4}

Given: 

                f\left ( x \right )=x^{2}+4,f:R\rightarrow R_{+}\rightarrow \left [ 4,\infty \right ].

Hint:

Bijection function should be fulfil the injectivity and surjectivity.

Solution:

Let x,y be two elements of the domain \left ( a \right ).

\! \! \! \! \! \! \! \! \! \! f\left ( x \right )=f\left ( y \right )\\\\x^{2+4}=y^{2}+4\\\\x^{2}=y^{2}\\\\x=y

So fis one-one.

Let  y be in the co-domain\left ( a \right ) such that

                \! \! \! \! \! \! \! \! f\left ( x \right )=y\\\\x^{2}+4=y\\\\x^{2}=y-4\\\\x=\sqrt{y-4}\epsilon \: R

                f is onto, so f is bijection.

                \! \! \! \! \! \! \! \! f^{-1}\left ( x \right )=y\\\\x=f\left ( y \right )\\\\x=y^{2}+4\\\\x-4=y^{2}y=\sqrt{x-4}\\\\f^{-1}\left ( x \right )=\sqrt{x-4}                                                                                                                                       … (i)

               

Posted by

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