Domain of sinx−ex  is

Let f(x)=sinx−ex                    Where h(x)=ex Let f(x)=g(x)−h(x)               h(x)  is defined if x≥0  Where g(x)=sinx                         ∴  Domain of h(x)=[0,∞) Domain of g(x)=R ∴  Domain of f(x)={domain  of  g(x)}∩{domain  of  h(x)} =R∩[0,∞) =[0,∞) ∴  Domain of f(x)=[0,∞)