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  • If <img alt="f^{-1}\left(x\right)=sin\:x\:and\:g^{-1}\left(x\right)=x^3" src="http://entrancecorner.oncodecogs.com/gif.latex?f%5E%7B-1%7D%5Cleft%28x%5Cright%29%3Dsin%5C%3Ax%5C%3Aand%5C%3Ag%5E%

If f^{-1}\left(x\right)=sin\:x\:and\:g^{-1}\left(x\right)=x^3  . Then (gof)^{-1}\:\:x=

Option: 1

\sin x^3


Option: 2

(\sin x)^3


Option: 3

\sin x\sqrt[3]{x}


Option: 4

(\sin x)^{1/3}


Answers (1)

best_answer

As we have learned

Property of inverse

If f:A\rightarrow B\ and\ g:B\rightarrow C are two bijections, then  (gof)^{-1}=f^{-1}og^{-1}

 

Now

 gof^{-1}= f^{-1}og^{-1} = f^{-1} (x^3)

= \sin (x^3)= \sin x^3

 

Posted by

Pankaj Sanodiya

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