Using the R package `MASS`, I transformed a variable, lets call it $V$ into another variable called $X$ with $\lambda = 1.25$.

Now, the `BoxCox transformation` has the following shape:

$X = (V^\lambda - 1) / \lambda$

So the reverse transformation is:

$V = (\lambda X + 1)^{1/\lambda}$

With $\lambda = 1.25$, $V < 1$ imply that $X < 0$. However, the reverse transformation only works for positive values with $\lambda = 1.25$. I therefore want to add a constant to $X$ before doing the reverse transformation. Lets call it $Z$ such that :

$Z = \begin{cases}1 - \mbox{min(X)} , & \mbox{if min(X) < 0}\\ 0 , & \mbox{otherwise}\end{cases}$

Then the reverse transformation becomes:

$V + E = (\lambda X + \lambda Z + 1)^{1/\lambda}$ 

**Question:** What transformation do I apply to $V + E$ in order to get back the true value $V$ only ?