What to Do with Inverse Functions in Complex Cases?

[transgalactic]

i need to find the inverse function of these:
http://img522.imageshack.us/my.php?image=63348338nf8.gif

i know that if y=sinx
then its inverse whould be x=arcsin y

but the first case has two = signs
and the second one is a split function

what to do in these cases?

 

[Avodyne]

In the first case, you are being given the definition of the hyperbolic tangent. So one answer is x = arctanh y. But presumably you are to ignore this, and solve it as if you were given only the function on the far right.

As for the split function, for each specified range of x, what is the corresponding range of y?