Two things regarding hyperbolic tangent (tanh(x)):
1) What is the inverse function of tanh(x)?
Apparently it is NOT artanh(x).
I need to know how to "undo" a tanh(x) function. Please help.
2) In my grapher, artanh(1) does not exist (is undefined, invalid or whatever).
Yet when I plug in artanh(sin(x)^2+cos(x)^2), which should be the same, I get weird splotches.
Is the grapher getting confused, or does there really exist a difference between 1 and sin(x)^2+cos(x)^2 vis-a-vis artanh(x)?
Your demonstration is very useful to me. Many thanks.
An important question remains, however: Is artanh(x) the inverse function of tanh(x)?
The wikipedia definition of inverse function is:
"If ƒ is a function from A to B then an inverse function for ƒ is a function in the opposite direction, from B to A, with the property that a round trip (a composition) from A to B to A (or from B to A to B) returns each element of the initial set to itself."
By this definition, for x=1, artanh(x) is NOT the inverse function of
Perhaps this simply means that tanh(x) is not invertible?