Normalize and denormalize

Question

I have this Function

y = (x - min) / (max - min)

which normalizes my values. Now i want to know how to denormalize them, how does the new function look like?

Answer 1

Suppose the minimum is achieved at $x_1$ and the maximum at $x_2$. It is easy to write a linear interpolant: in fact, just use point-slope form:

$$ y - M = \frac{M - m}{x_2 - x_1} \left( x - x_2 \right) $$

and you have a function that returns the raw scores instead of the normalized values.