Let f, g are differentiable function su...

Let `f, g` are differentiable function such that `g(x)=f(x)-x` is strictly increasing function, then the function `F(x)=f(x)-x+x^(3)` is
(A) strictly increasing `AA` x in R
(B) strictly decreasing `AA` x in R
(C) strictly decreasing on `(-oo,(1)/(sqrt(3)))` and strictly increasing on `((1)/(sqrt(3)),oo)`
(D) strictly increasing on `(-oo,(1)/(sqrt(3)))` and strictly decreasing on `((1)/(sqrt(3)),oo)`

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