
range for e^f(x)
Hi all, just looking at this function
I have found the yintercept to be and x intercepts to be
These are correct.
I have also found a cusp type maximum at (1,1) . Therefore
This range was found using trial and error, is there a way to find this range other way for this type of function?

First, of course, x1= x+ 1. Since that is never negative, is never less than 1, is never larger than 1 and so is never larger than 1. Of course when x= 1, x1= 0, and y= 1. Since x+1 can be arbitrarily large and is an increasing function, y can be any negative number. That gives the range as

Thank you, this method seems obvious now it has been presented.