Does Arctanh Go to Infinity When Its Argument Approaches Infinity?

[rmiller70015]

So, I'm doing a problem where I take arctanh to a limit, and I was wondering if the arctanh function goes to infinity if the argument inside of the function goes to infinity when passing through the limit.

 

[mathman]

Is the argument real or complex? For real numbers, |tanh| ≤ 1. If the argument for arctanh is not in the domain [-1,1], then arctanh must be complex.