Converting dependable variable to independant and vice versa

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In summary, the conversation was about finding x as a function of F in a mathematical method. The person had tried using Mathematica but did not get a result. Another person suggested a method of multiplying the equations and solving for x, but the solution was too large.

Is this possible to solve this analytically?

  • Absolutely Yes.

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  • nope, only possible numerically.

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  • May be

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  • #1
venki_k07
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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
 
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  • #2
can you mutliply them before asking computer to solve for x?
 
  • #3
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.
 
  • #4
Yup. That works, but gives a very huge solution which can be used to solve my system.

Thank you very much.
 
  • #5


Hello Venkatesh,

Thank you for reaching out for help with your function. It seems that you are trying to convert the dependent variable F to an independent variable x. This is possible through the process of inverse function, where the dependent and independent variables switch roles.

To find x as a function of F, you can start by solving for x in your original function F(x). This will give you two equations, one for F1 and one for F2. Then, you can combine these two equations to get an equation for x(F). This can also be done using the inverse function property in mathematica.

However, it is important to note that not all functions have an inverse function, so it may not always be possible to convert the dependent variable to an independent one. In these cases, you may need to use numerical methods to approximate the value of x for a given F.

I hope this helps. Good luck with your function!
 

1. How do you convert a dependable variable to an independent variable?

To convert a dependable variable to an independent variable, you will need to perform a reverse causation analysis. This involves identifying potential confounding variables and controlling for them to establish a causal relationship between the variables.

2. What is the purpose of converting a dependable variable to an independent variable?

The purpose of converting a dependable variable to an independent variable is to establish a causal relationship between the two variables. This allows researchers to make predictions and draw conclusions about the effects of the independent variable on the dependent variable.

3. Can an independent variable become a dependable variable?

Yes, it is possible for an independent variable to become a dependable variable in certain situations. For example, if a study is examining the effects of a treatment on a specific outcome, the treatment would be the independent variable. However, if the study is examining the effects of the outcome on the treatment, the treatment would then become the dependent variable.

4. How do you determine which variable is independent and which is dependent?

The independent variable is the variable that is manipulated or controlled by the researcher. It is typically plotted on the x-axis in a graph. The dependent variable is the outcome or result of the independent variable and is usually plotted on the y-axis in a graph.

5. What are some common methods for converting a dependable variable to an independent variable?

Some common methods for converting a dependable variable to an independent variable include conducting experiments, using statistical techniques such as regression analysis, and using control variables to account for potential confounding factors. It is important to carefully design the study and control for any potential confounders to ensure a strong causal relationship between the variables.

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