Laplace Transform Analysis

[S_David]

Hello,

Suppose that:

F_X(x)=1-\mathcal{L}^{-1}\left(\frac{M_Y(s)}{s}\right)

But

M_X(s)=s\mathcal{L}\left(F_X(x)\right)=s\mathcal{L }\left(1-\mathcal{L}^{-1}\left(\frac{M_Y(s)}{s}\right)\right)=1-M_Y(s)

where \mathcal{L}^{-1}\text{ and }\mathcal{L} are the inverse and forward Laplace transform operators. Is what I did right, or there is something error and I do not know about?

Thanks in advance