Let [], and {} denotes the greatest integer function and fractional function, consider the following statements.
`S_(1)` : The range of `({x})/(1+{x})` is `[0, (1)/(2))`
`S_(2)` : The range of `[(1)/(sin {x})]` is `Z^(+)`
`S_(3)` : The range of `(x^(2) + 2)/(x^(2) + 3)` is `[(2)/(3), 1)`
`S_(4)` : The range of `sin sqrt((pi^(2))/(16) - x^(2))` is `[0, (1)/(sqrt(2))]`
Which of the following is the combination of true statements ?

Options

A. `S_(1), S_(2), S_(3), S_(4)`
B. `S_(1), S_(2)` only
C. `S_(2), S_(3)` only
D. `S_(1), S_(3)` only

Answer

A