Find the domain and range of `f(x)="sin"^(-1)(x-[x]),` where [.] represents the greatest integer function.

Explanation

We have `f(x)="sin"^(-1)(x-[x])=sin^(-1){x}`
We know that `{x} in [0,1)`
For these values of `{x},sin^(-1){x}` is well defined .
So, domain of the function is R.
Now, `0 le {x} lt 1`
`implies sin^(-1)0 le sin^(-1){x} lt sin^(-1) 1`
`implies 0 le sin^(-1){x} lt pi//2`
Hence range of the functions is `[0,pi//2)`