Let f:R→ R be a periodic function such that f(T+x)=1+1−3f(x)+3(f(x))2−(f(x))31/3 where T is a fixed positive number, if period of f(x) is kT, then the value of k is ..

Given, f(T+x)=1+(1−f(x))31/3=1+(1−f(x))f(T+x)+f(x)=2---if(2T+x)+f(T+x)=2----ii(2)−(1)=f(2T+x)−f(x)=0f(2T+x)=f(x)Also, T is positive and least ,therefore period of f(x)=2Tk =2