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sin^-1[x+1] + cos^-1[x]= g(x)f(x)= cos^-1(cosx)no of solutions of f(X) +g(x)[] represents greatest integer

juhi ranjan , 13 Years ago

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1 Answers

Arun Kumar

Last Activity: 10 Years ago

Hello Student,

$\\g(x)=sin^{-1}[x+1] + cos^{-1}[x] \\f(x)= cos^{-1}(cosx) \\-1 \leq [x+1] \leq 1 \\=>-2 \leq [x] \leq 0 \\-1 \leq [x] \leq 1 \\$taking union$ \\-1\leq [x] \leq 0 \\=>x \in [-1,1) \\$so $f(x) = sin^{-1}0 + cos^{-1}1=0 \\$or $f(x) = sin^{-1}1 + cos^{-1}0={\pi \over 2} \\$depending upon x g(x) can be found out too$$

Now you please specify the equation properly because for roots it has to be equated with something.

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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