sudac;
Yes, they can be joined by welding. F1 is carbon-moly steel, while F11 is a Cr-Mo low alloy steel (1.25% Cr- 1/2% Mo).
You have various options for filler metal selection; either E70 or E80 series weld rod to match either base metal. The requirements for preheat and post heat should be dictated by the higher alloy base metal, in this case F11.