Find the range of $f(x) = \sin^{-1}(x - [x])$, where [.] represents the greatest integer function.
Answer & explanation
Correct answer: option 1
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 $[0,π/2)$