Yes, It is a bug Indeed.
Thanks for reporting.

Fixed in this PR:  https://github.com/sympy/sympy/pull/9231
Please have a look.

*Reference:*
http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
http://www.wolframalpha.com/input/?i=ArcCosh%5B-z%5D

On Tuesday, March 31, 2015 at 8:10:18 PM UTC+5:30, Arnaud Usciati wrote:
>
> Hello everybody,
>
> I tried values with acosh function and I found an issue.
> Suppose x = symbols('x', real=True) and f = lambda x: acosh(-x).
>
> For instance :
> > Input : f(1)
> > Output : I*pi
>   --> That's OK
>
> > Input : f(-1)
> > Output : 0
>   --> That's OK
>
> But f(x) returns -acosh(x) instead of acosh(-x) ! It's wrong because 
> 'acosh' it's certainly not odd !!
>
> Arnaud
>
>
>

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