Ok I get it now, thanks.

Alpha gave the correct result assuming x is not the isolation variable.

The result I am expecting does not extend to the imaginary numbers. I perhaps should have given some back ground info, my mistake. In this context just strict the Domain/ Range to real numbers. What I was looking for was just a solution to a seperable differential equation, which would give me a velocity-time graph until the terminal velocity is reached. Anyways I managed to do the plot using another application. And I took the inverse of the function using a pen lol. Also in this context {a,b,c} are variables independant of x. For instance "c" is the mass of a skydiver. The initial reason why I used Alpha was that I did not want to lose time with basic calculations. I knew the physics behind the phenomenon so I recognized that the result I received was impossible to obtain and was wrong. And of course you are right about restricting domains when using tan(x), however unlike tan(x): tanh is invertible for the whole domain it is defined on. Of course this is with real numbers only, ( I dont really know how its extension on the complex plane looks like) but the taylor series expansion of tanh(x) can possibly be used to get an idea... Though I am not sure, just guessing. In the end It just surprized me that Wolfram Alpha failed to comply an algorithm even GeoGebra could comply. What i was trying to obtain was as simple as that. By the way the plot of that inverse function which started this in the first place is as follows where constants {a,b,c} are put in place. y axis represents the horizontal velocity, x axis represents time.

Finally and off the topic as well I didn't really understand what you meant by saying i^1,i^2,i^3,i^4 are not imaginary, could you explain it a little further. Because I thought that everything we know in current mathematics is actually defined under the complex numbers. you caught my attention.

without having graphed it myself i'll underline what sander said

functions that "pass tests" are invertible, not all relations are invertible

you have many variables maybe dependant or independant, and i don't see what the graph looks like

a typical inversion routine from Algebra needs dependant y and independant x as arguments to it, and it appears Mathematica asks for this and you didn't provide it, and that you didn't use mathematica but a "guesser"; however the guesser cannot convey the information to you that your input is problematic in many ways

you havent told Mathematica anything about these mystery variable, and it is likely cautiously and probably correctly avoiding answers that would not be true in "the general case" of what you gave it

graph the solution using mathematica, upload the graph, so we can see it breaks no rules (quite plainly easily by view) and can be inverted

is f() one to one? are your variables following the rules of inversion (you didnt say) ? which variable is taken as f(x)=y?

the graph i see is like this, and i would say it is not invertible in general, but that regions of it may be

Attachments:

I ran the same algorithm, this time with Geogebra, the result it gave is the way I predicted it to be. Though tomorrow I will try it with my TI as well...Just to be sure. Then I will give a call to the Tech Support. Thanks for the advice.

Should I inform some body?

Oh, I already found the inverse of the function myself' it is uploaded at the bottom of the page. I just wanted to know why the "invert' function failed to comply properly.

Until now it always has taken "x" as the variable' and others as constants. Though I guess you are right, because as I decreased the number of unknowns it got back to normal.