1.

The range of `sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2]`, where [.] denotes the greatest integer function, is`{pi/2,pi}`(b) `{pi}`(c) `{pi/2}`(d) none of theseA. `{(pi)/(2),pi}`B. `{pi}`C. `{(pi)/(2)}`D. None of these

Answer» Correct Answer - B
`[x^(2)+(1)/(2)]=[x^(2)-(1)/(2)+1]=1+[x^(2)-(1)/(2)].`
Thus, from domain point of view,
`[x^(2)-(1)/(2)]=0,-1 or [x^(2)+(1)/(2)]=1,0`
i.e., `f(x)=sin^(-1)(1)+cos^(-1)(0) or sin^(-1) (0) + cos^(-1)(-1)`
` or f(x)={pi}`


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