# Math Help - Help with function reconstruction

1. ## Help with function reconstruction

Hi,

I'm stuck with this problem to reconstruct a function:

$
\forall i \in 1..N \bigg\{ \begin{array}{l}
f(x_i) = i \\
f(2*x_i) = g(i)
\end{array}
$

I know function $g(x)$ and I would like to get an approximation of $f(x)$. Both f and g are monotonic increasing. Any hint on where to start would be greatly appreciated.

I don't know if this is the correct forum for this post, so please redirect me to another one if necessary.