Converting dependable variable to independant and vice versa

[venki_k07]

Hello guys,
First of all, thanks for looking at this post and trying to help me.

I have function which is shown below,

F1= (ε1-√(1+(ε1 μ1-1)x^2))/(ε1+√(1+(ε1 μ1-1)x^2));
F2= (ε2-√(1+(ε2 μ2-1)x^2))/(ε2+√(1+(ε2 μ2-1)x^2));
F=F1*F2;
Here, F is a function of x --> F(x)
I need to find x(F) , x as a function of F. Is there any mathematical method for doing this.?
x(F1) and x(F2) is possible using mathematica and it is easy too. But i don't know how to find x(F).

I tried this in mathematica but it is not giving me any result.

Thanks,
Venkatesh

 

[algebrat]

can you mutliply them before asking computer to solve for x?

 

[haruspex]

Writing as F1 = (a-√b)/(a+√b), F2 = (c-√d)/(c+√d),
F(a+√b)(c+√d) = (a-√b)(c-√d)
(F-1)(ac+√(bd)) = - (F+1)(a√d + c√b)
(F-1)²(a²c²+bd+2ac√(bd)) = (F+1)²(a²d+c²b+2ac√(bd))
(F-1)²(a²c²+bd) - (F+1)²(a²d+c²b) = 8Fac√(bd)
Squaring again produces a quadratic in b and d. The only x terms are in the form of x² within b and d. There's an uncancelled b²d² term and nothing higher, therefore the polynomial is a quartic in x².

 

[venki_k07]

Yup. That works, but gives a very huge solution which can be used to solve my system.

Thank you very much.