19.设函数f(x)=1−2x2f(x)=1-2x^{2}f(x)=1−2x2,g(x)=x2−2xg(x)=x^{2}-2xg(x)=x2−2x,若F(x)={g(x),f(x)⩾g(x)f(x),f(x)<g(x)F(x)=\left\{\begin{array}{l}{g(x),f(x)\geqslant g(x)}\\ {f(x),f(x)<g(x)}\end{array}\right.F(x)={g(x),f(x)⩾g(x)f(x),f(x)<g(x),则函数F(x)F(x)F(x)的最大值为((( )))