The range of the function, fx=ex-exex+ex

fx=ex-exex+ex=0,                 x≥0 ex-e-xex+e-x,  x<0Clearly, f(x) is identically zero if x≥0                       (1)If x<0,   let   y=fx=ex-e-xex+e-x or  e2x=1+y1-y   x<0     e2x<1    or   00    and    1+y1-y<1or   y+1y-1<0   and   2y1-y<0i.e.,   -11or       -1