A function s(x) is defined as g(x)=14f2x2−1+12f1−x2 and f′(x) is an increasing function. Then g(x) is increasing in the interval

g′(x)=xf′2x2−1−xf′1−x2=xf2x2−1−f1−x2  ⇒ g′(x)>0If x>0,2x2−1>1−x2 (as f ' is an increasing function)or    3x2>2 or x∈−∞,−23∪23,∞or    x∈23,∞If x<0,2x2−1<1−x2or    3x2<2 or x∈−23,23 or x∈−23,0