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 these

Options

A. `{(pi)/(2),pi}`
B. `{pi}`
C. `{(pi)/(2)}`
D. None of these

Answer

B

Explanation

`[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}`