1. The problem statement, all variables and given/known data Let f(x)=e^(-x)-x ,, x belongs to R Find the domain of f inverse 2. Relevant equations Domain of f inverse = range of f 3. The attempt at a solution we have : -inf < x < inf -inf < -x < inf .... (1) 0 < e^(-x) < inf .... (2) By adding (1) and (2) : -inf < e^(-x) - x < inf So domain of f = R = range of f inverse. Is this correct? Can I add the inequalities together?