f has to be monotonic and increasing, and such as f(x) < 0 if x < 0 , and f(x) > 0 if x > 0 (note the strict inequalities, that makes it a condition slightly s

f has to be monotonic and increasing, and such as f(x) < 0 if x < 0 , and f(x) > 0 if x > 0 (note the strict inequalities, that makes it a condition slightly stronger than monotonic).