How can we solve this integral equation for f(t) given g(x) is known?

[Karlisbad]

i would need to solve the integral equation..

$$g(x)=\int_{-\infty}^{\infty}dte^{ixf(t)}$$

the unknown function is f(t) g(x) is known, appart from using a numerical cuadrature method for the integral, what else can i do?.. could we prove if the function f(t) will exist or if it won't have any solution??..thanx.

 

[DeadWolfe]

"the unknown function is f(t) g(x) is known"

*head explodes*