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Analyse g(x)=sin^-1[x+1] + cos^-1[x] f(x)=cos^-1(cosx)

Analyse 
g(x)=sin^-1[x+1] + cos^-1[x]
f(x)=cos^-1(cosx) 

Grade:9

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 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$
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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