Find the range of $f(x) = \sin^{-1}(x - [x])$, where [.] represents the greatest integer function.

$[0,\frac{π}{2})$

We have $f(x) = \sin^{-1}(x - [x])=\sin^{-1}\{x\}$

We know that $\{x\} ∈ [0, 1)$

For these values of {x}, $\sin^{-1}\{x\}$ is well defined.

Now $0≤\{x\}<1$

$⇒\sin^{-1}0 ≤ \sin^{-1}\{x\}<\sin^{-1}1$

$⇒0 ≤ \sin^{-1}\{x\}<π/2$

Hence range of the function is $[0,π/2)$