about the inverse function

i have read about the inverse function form wiki but i still have poblem understanding them.
according to me:
a function is a relationship of two or more variables i.e let us take i.e x=f(t) meaning:x is dispalcement taking place at various different time "t "
i.e x=sint then i can imagine a continuously changing dispalcement with respect to time that is nothing but a sine wave.here ""x"" is dependent variable & ""t"" is independent variable.
now, how should i imagine it's inverse i.e t=f(x) how can i say that t is dependent on x?? this sound very sloppy to imagine..
can anyone expalin it properly??

Formally, if x = sin(t), then t = arcsin(x). If you look at the graph, you notice that the function be only inversed with restrictions. But the function exists, you can e.g. use your pocket calculator to get the result.

but, if i think just casually without going into maths then it shows me that i am trying to draw a graph where i am considering time to be dependent on distance(x) how do i imagine this then??

Dependent and independent variables are mathematical terms to define which is the argument of a function (independent) and its result (dependent). This because once you decide the value of the independent variable (that must be inside the domain of the function), automatically the value of dependent variable is fixed by the function.
You are instead speaking about the physical meaning.
Your direct function x=f(t) says: at time "t" the displacement was "x"
The inverse function instead says: when the displacement was "x" the time was "t". That means knowing the displacement you can calculate back the time. Physically "t" is always independent from "x".

The problem here, is that your function is periodic then the inverse can be calculated only over a restricted domain of the function.
We know that sin(t) repeats over a period of \[2\pi\], if we do not restrict the inverse to a such variation (f.i. \[-\pi\],\[\pi\]) the inverse will lead to many "t" for the same "x" (that is outside the definition of function).
So with this function that connects t and x, given the displacement "x" you can't recover the exact time. For instance

t=13.2 (\[4.2\pi\]) ==> x=0.5878
going back x=0.5878 ==> t=0.628 (\[0.2\pi\])

you can see the result has been wrapped in the \[-\pi\],\[\pi\] range

thanks please see this thread:https://www.edaboard.com/threads/309307/

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thanks please see this:http: https://www.edaboard.com/threads/309307/

Disha Kaarnataki,

how should i imagine it's inverse i.e t=f(x) how can i say that t is dependent on x?? this sound very sloppy to imagine..
can anyone expalin it properly??

Click to expand...

t=f(x). What is so hard to imagine that it takes more time to travel a farther distance?

Ratch

how can something be dependent on time???????????????? when displacement let us take sine wave is dependent on time then how can i say that time is dependent on displacement????

Disha Karnataki said:

how can something be dependent on time???????????????? when displacement let us take sine wave is dependent on time then how can i say that time is dependent on displacement????

Click to expand...

That is easy to answer. A transportaton vehicle travels more distance if the travel time is greater. Conversly, it takes more time to travel a greater distance.

Ratch

ok, consider you have a coil and magnet moving in and out of the coil (FARADAY'S EXPERIMENT) now i will say that as per the flux linking the coil there will be voltage induced in the coil. If i try to plot the graph then certainly i will have flux linking the core to be independent variable and the voltage induced will be dependent variable. now how probably will be the inverse???
ok let me guess you will tell it as :let the voltage induced be=xyvolts amount so the amount of flux that would have had linked will be =zyweber is it???
but let me tell you that for inverse function here voltage becomes independent variable and flux becomes dependent variable.So it means that what is the change in flux for the given change in voltage. And here how will u tell me the dependencies because flux is in control of the person who is continuously moving the magnet. How can the voltage induced in the coil control the flux produced by someone who is moving the magnet??????????????????? this all sounds absurd to me!!!!!!!!!!... i donot know about you........

How can the voltage induced in the coil control the flux produced by someone who is moving the magnet??????????????????? this all sounds absurd to me!!!!!!!!!!... i donot know about you........

Click to expand...

1. Calm down
2. Review forum rules about allowed post style

The error of reasoning is associating abstract mathematical operations with real physical events, I think. You can do this in some cases, but not in all.

Regarding relation of magnetical flux and induced voltage (U =a*dB/dt), it can be well inversed to calcukate the flux generated by a an applied voltage integral. B = 1/a integral (U dt)

As I said in my post #4 dpendent and independent variable are mathematical terms.
The physical meaning can be different. In the experiment you cites the output volatge is a function of the flux, the flux is made varying by a person that moves the magnet in the coil.
The inverse function tell you what was the flux variation that caused the voltage I read
Going back to the mathematical term, in this last case the voltage is called independent variable because I can set it at any value I want to know the flux variation that caused that output voltage. The flux is instead called dependent variable because it is the output of the function. Don't make confusione between mathematics and physics.