Expert: Ahmed Salami - 10/26/2004

Question
 f(x)= tan hx  Rf=?  Df=?
 g(x)= cot hx  Rg=?  Dg=?      
 tnx

Answer
Hi Mariam,
I'm assuming you are referring to hyperbolic tangents and cotangents i.e tanh x and coth x.
tanh x = e^x - e^(-x)/e^x + e^(-x)
For very large positive values of x, e^(-x)approaches zero and tanh x therefore approaches
e^x - 0/e^x + 0 = 1
For very large negative values of x, e^x approaches zero and tanh x therefore approaches
0 - e^(-x)/0 + e^(-x) = -1
tanh x therefore lies in between -1 and 1. Also x can take all values.
So for tanh x, the range R = -1 <= tanh x <= 1
and the domain D = -# <= x <= #
where # represents infinity
For coth x, the range R = -# <= coth x <= -1 and
1 <= coth x <= #
this means that coth x can take all values except for those between -1 and 1
the domain D = -# <= x <= #

I hope you understand it. You can always get back to me.
Regards.