I'm slow studying the math.
I'm trying to calculate the numbers with given start and end number.
For example,
What if there are 256 numbers as 0,1,2,3,4,5...255.
and I just only know if 0 then 9 and if 255 then 3.
Then how do we calculate between the numbers (1), (2), (3)..(254)?
more example, what if there are 4 numbers as the below.
1,2,3,4
What if we give start and end number for this example. (1)= 1 and (4)=4 then we can calculate (2)=2, (3)=3. but what if start without 1, then how do we know?
There are many answers to your problem.
If you only know f(x) for two values of x, you have many different choices for other values of f(x).
You need a formula for f(x) or you may interpolate your data to fit a curve through your data.
For example You may fit a straight line through the two points $(0,9)$ and $(255,3)$ that you have and use that to find f(x) for other values.