dibcota[k_] := Plot[{F[x, k],
  G[x, k]}, {x, 2^-(k + 1), 2^-k}, PlotRange -> {0,
    1}, AspectRatio -> Automatic, DisplayFunction -> Identity]

a = dibcota[0]; b = dibcota[1]; c = dibcota[2]; d = dibcota[3];

Show[a, b, c, d, DisplayFunction -> $DisplayFunction]