Domain (D) and range (R) of `f(x)=sin^(-1)(cos^(-1)[x]),` where [.] denotes the greatest integer function, is `D-=x in [1,2],R in {0}` D`-=x in 90 ,1],R-={-1,0,1}` `-=x in [-1,1],R-={0,sin^(-1)(pi/2),sin^(-1)(pi)}` `-=x in [-1,1],R-={-pi/2,0,pi/2}`

Options

A. `D-= x in [1,2), R-={0}`
B. `D-= x in [0,1], R={-1,0,1}`
C. `D-= x in [-1,1], R-= {0,sin^(-1)((pi)/(2)), sin^(-1)(pi)}`
D. `D-= x in [-1,1], R-={-(pi)/(2),0,(pi)/(2)}`

Answer

A

Explanation

When `[x] =0,` we have ` sin^(-1)(cos^(-1)0)=sin^(-1)(pi//2),` not defined.
When `[x] =-1,` we have ` sin^(-1)(cos^(-1)(-1))=sin^(-1)(pi),` not defined.
When `[x]=1`, we have `sin^(-1)(cos^(-1)1)=sin^(-1)(0)=0,`
Hence, ` x in [1,2)` and the range of functions is {0}.