0

Let $\sum_{i=1}^{n}g(x_{i}) = G$. What is important is that I do't know the value of $g(x_{1}),...,g(x_{n})$, and I only know the value of their summation.

How I can compute the answer of the following summation based on $G$ $$\sum_{i=1}^{n}g(x_{i})e^{x_{i}}$$

Hasan Heydari
  • 1,187
  • 1
  • 8
  • 22
  • Why do you think the second sum depends only on the first, independent of the $g(x_i)$? Does this question come up in some context you haven't told us about? Please edit the question to clarify. – Ethan Bolker Jun 29 '18 at 20:33
  • @EthanBolker As I said in the question, I don't know the value of $g(x_{i})$ $(1\leq i \leq n)$, but I know the value of their sum. So I want an answer based on their sum. – Hasan Heydari Jun 29 '18 at 20:36
  • 1
    Do you know (or better: can choose) either $g$ or $x_i$? Right now it's 100% impossible. – orlp Jun 29 '18 at 20:38
  • Well you can solve it for special cases of $x_i =0$ and $n=1$. – Ali Jun 29 '18 at 20:44
  • @orlp, Unfortunately, No. – Hasan Heydari Jun 29 '18 at 21:02
  • Then this problem is certainly unsolvable with the information given. – John Barber Jun 29 '18 at 21:04
  • What is the context of this problem? Is it just something you made up, or does it come from a mathematics text, or a physical problem, or what? – John Barber Jun 29 '18 at 21:06

1 Answers1

2

Assuming you don't know either $g$, $x_i$, it is impossible. It is possible for example that $g(x) = x$.

Then $G = 2$ for both $x = (2, 0)$ and $x = (1, 1)$. So you can't distinguish between those two cases.

But one has answer $2e^2$ while the other has answer $2e$.

orlp
  • 10,508