f(x) is increasing on (e, ∞) and decreasing on (0, e)
f(x) is increasing on (e, ∞) and decreasing on (0, e) - {1}
f(x) is increasing on (0, ∞) and decreasing on (-e, 0) - {-1}
f(x) is increasing on ( -e, ∞) and decreasing on ( - ∞, - e) - {1}
f(x) is increasing on (e, ∞) and decreasing on (0, e) - {1}