Swapping the X and Y position of y=tanh(x)

[Aridus92]

Is swapping the position of x and y in y=tanh(x) possible? If so, can someone please explain the steps to do so?

 

[ksdhart2]

Erm... sorry, but I don't think I understand what you mean. If you mean just interchanging the symbols, then there's absolutely nothing stopping you from doing so. You can just say x = tanh(y), and you'll now have x as a function of y and the graph will have every (x,y) coordinate replaced with the corresponding (y,x) and it will be rotated 90 degrees. If you mean something else, you'll need to clarify your intent.

 

[Aridus92]

I'm trying to make y=tanh(x) into an equation such as x="so and so" where both equations are completely equivalent to each other. Basically, I want to manipulate the original equation of y=tanh(x) so that it becomes in respect to x. For example, in the equation y = x^2, if I wanted to manipulate the equation so that it because x="something", I would simply take the square root of y and x so that the equation would look like x=sqrt(y). That's what I'm trying to do with the equation y=tanh(x)

 

[mmm4444bot]

You want the inverse hyperbolic tangent function: artanh(x)

Sometimes, it's written tanh^-1(x) or arctanh(x) or atanh(x).

If y = tanh(x) then x = artanh(y)

If you google keywords hyperbolic tangent function, you can find formulas for it, like this one:

artanh(x) = 1/2*ln[(1 + x)/(1 - x)]

 

[Aridus92]

You want the inverse hyperbolic tangent function: artanh(x)

Sometimes, it's written tanh^-1(x) or arctanh(x) or atanh(x).

If y = tanh(x) then x = artanh(y)

If you google keywords hyperbolic tangent function, you can find formulas for it, like this one:

artanh(x) = 1/2*ln[(1 + x)/(1 - x)]

Thank you very much, that's all I was looking for!

 

[mmm4444bot]

… trying to make y=tanh(x) into an equation such as x="so and so" where both equations are completely equivalent to each other.

Functions and their inverses are not "completely equivalent", but each completely determines the other.

… For example, in the equation y = x^2, if I wanted to manipulate the equation so that it because x="something", I would simply take the square root of y and x so that the equation would look like x=±sqrt(y).

Be careful, with inverses. They often come piecewise, like sqrt(x) and -sqrt(x), because of domain restrictions. :cool: