function analisys

[Brainstorm]

Salutations, I'm not very good in English but I'll be there ^^'
So, I have a very interesting problem that i don't even know how to start, I'll make it simple for you so I don't have to bet on my bad English.

x f(x)                 x f(x)                 x f(x)
1 2                    1 1                    6 2
2 4                    2 4                    7 14
3 6                    3 9                    8 56
4 8                    4 16                   9 168
...   f(x) = 2x;       ...    f(x) = x2;      10 420
                                              11 924
                                              12 1848
                                              13 3432
                                              14 6006
                                              15 10010
                                              ...          f(x) = ?

I want to build a program that analyses the input and output, and "discovers" the function, i know it's possible and I really want to learn this, if anybody has any information about this i would appreciate, thanks in advance.

[Skillless]

No idea how to do this, but you should know that this will be extremely hard and it will take ages if you use even a slightly big function ((cos(x)*5+1)²+x)³

And your english is fine =P

[Brainstorm]

Thanks for the reply skillless, but I need information about this, the proccess name, the math behind it, anything so I can start searching around and learn myself if it is impossible or not.

[ne555]

You could approximate the function with a polynomial (Lagrange, Splines) or trigonometric (Fourier Series)
It's called interpolation

[Brainstorm]

thanks ne555, I'm searching about those.
http://www.solvemymath.com/online_math_calculator/interpolation.php <-- found this ^^'