If f(x)=log(100x)((2log(10)x+2)/(-x));g(...

If `f``(x)=log_(100x)``((2log_(10)x+2)/(-x));g(x)={x}` where `{x}` denotes the fractional part of x. If the function `fog(x)` exists then the maximum possible range of `g(x)` .
(1) `(0,10^(-3))uu(10^(-3),10^(-1))`
`(2) (0,10^(-2))uu(10^(-2),10^(-1))`
`(3) (0,10^(-3))uu(10^(-3),10^(-2))`
`(4) (0,10^(-1))uu(10^(-1), 1)`

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