Given functions are, f(x)=ex−x and g(x)=x2−x f(g(x))=e(x2−x)−^2−x) Given f(g(x)) is increasing function. ∴(f(g(x)))′=e(x2−x)×(2x−1)−2x+1 =(2x−1)e(x2−x)+1−2x=(2x−1)[e(x2−x)−1]≥0 For (f(g(x)))′≥0, (2x−1)&[e(x2−x)−1] are either both positive or negative