we can divide the function into two functions if x<0 and x>1

this for y<0 and y>1 this is the range, the domain here is all real numbers

if 0<x<1

this when 0<y<1 this is the range, that means x will take the values when 1-e^x is larger than e^x

0,1 the function is not defined so these points are not included in the domain of f(x)( the range of )