I am a beginner, and I have questions concerning some functions.
First, if I do:
Assuming[0 < a < 1, Reduce[(1 - Exp[x])^2/a^2 < 1, x, Reals]]
I get this:
(a <= -1 && x < Log[1 - a]) || (-1 < a < 0 &&
Log[1 + a] < x < Log[1 - a]) || (0 < a < 1 &&
Log[1 - a] < x < Log[1 + a]) || (a == 1 && x < Log) || (a > 1 &&
x < Log[1 + a])
Why does M8 give me the solutions for a<0 and a>=1 if I assume that 0<a<1?
I have tried with $Assumptions and the result is the same. What should I do to get only this:
(0 < a < 1 && Log[1 - a] < x < Log[1 + a])
as a result?
Also I have seen that we can specify the domain of a variable using e.g. Element[x,Reals]. But how can I do if I want my domain to be some interval of Reals. For example I want x in [xmin,xmax] and a in ]0,1[. Is it possible using the function Element? Otherwise how should I do?
Thank you in advance for your answers.