Programmer cant rewrite/solve this equation

[UnluckyProgrammer]

New to this forum so i hope i post this in the right sub forum. I am a programmer and i am a bit rustic on my maths.
Ihave the following equation. i want to rewrite the equation so X is the outcome as in:
X = "the equation with Y and stuff"

I could rewrite some of the equation but now im stuck with the fact that x is inside and outside the sinus and cosinus hyperbolicus. how do I get them out of it without putting the other X inside an inverse sinus and inverse cosinus hyperbolicus?

it should be noted that the division X/B won't get bigger than 1 or smaller the zero.

if someone could give me the solution preferably with an explanation as to how this is done that would be highly appreciated.

 

[Steven G]

if someone could give me the solution preferably with an explanation as to how this is done that would be highly appreciated.
I am sorry but that is not how it works here. Where can off help but not complete answers with explanations. Rather we like to give leading hints to help you arrive to the correct solution.
Do you know how to tell if a function is 1-1? A function is 1-1 if and only if it passes the horizontal line test. That is no horizontal line passes through the graph in more than 1 place. Only in 1-1 functions can you try what you want to do. So find a graph of your function and only if it is 1-1 should you bother to continue looking for your answer.
Please do that 1st, post back your results and we will continue from there.

 

[Dr.Peterson]

Typically, when the variable is both inside and outside a transcendental function, I expect not to be able to solve algebraically. Do you have reason to think this can be solved? What is the context of your question? And are you certain that the equation is correct?

If I thought there should be a solution, I would look for an identity that might simplify [MATH]\sin\left(\cosh\left(1-\frac{x}{b}\right)\right)[/MATH] to an algebraic expression. But I have no reason to expect that.

 

[UnluckyProgrammer]

hey Jemo. this function does not pass the horizontal line test given the sin(cosh(u)) where u can range to any number. (fist graph). however when you limit the range of u to +0 to +1 it would for that range pass the test? and for that range it could be solved?

Dr.Peterson i have no reason to claim this can be solved algebraically. are there ways to solve this using other methods?

 

[Dr.Peterson]

As a programmer, have you studied numerical methods?

 

[UnluckyProgrammer]

if you meen differentiate, integration equations with lapace and or Z transforms. Yes, i study it but just to pass the exam, after that I never used it again and forgot about it, thinking i would not need it anymore.

do I need it now? (i can hear my math teacher hysterically laughing now ? )

 

[HallsofIvy]

No, that's not what "numerical methods" means!

 

[JeffM]

Numerical methods is the name for a branch of mathematics that generates approximate numerical answers when algebraic methods fail. It involves a lot of computation. For that reason, it is now done ( and has been since the late 1950s) mostly by computer.

However, you seem to want an algebraic answer.

[MATH]y = f(x) \iff x = g(y)[/MATH] within a limited domain.

Here is what I would do. Solve for y with five or six widely spaced x-values within the relevant domain. Now fit the resulting points to a polynomial, a trigonometric, and an exponential function using the y-values as the independent variable. Now take one more x-value in the relevant domain and calculate the corresponding y-value. Use that y-value in the three functions you came up with to see which one gives something closest to the x-value. Use that function.