I'm not very good at mathematics, so please bear with me.
How can you determine / define a function based on sets of values of its input and output parameters.
You have: $f(x_{1_1}, x_{1_2}, \ldots , x_{1_n}) = y_1$
$f(x_{2_1}, x_{2_2}, \ldots , x_{2_n}) = y_2$
...
$f(x_{n_1}, x_{n_2}, \ldots , x_{n_n}) = y_n$
You want: $f(x_1, x_2, \ldots , x_n) = a_1(x_1)^{b_1} + a_2(x_2)^{b_2} + \cdots + a_n(x_n)^{b_n}$
Let's assume that you have enough (how much is enough?) sets of input and output parameters.
What software could do this and how (excel, mathematica, r, ... ?). I'm looking for the simplest solution.
p.s. I need it only to define $f(x_1,x_2)=y$ function, but at the same time I'd like to learn more about all of this. Thank you for your time and answers.