What is it called when someone is showing lack of interest/no emotion?

Acting frigid is lacking emotional warmth: lacking warmth, friendliness, or enthusiasm.

And when someone is showing lack of interest and no emotion they are sometimes depressed.

Flat, frigid, and frosty are the only "f" synonyms that come to mind.

Maybe you were mistaken about the "f" so here is a list of some synonyms (or at least near synonyms) that might provide the word you're looking for: tepid, dispassionate, neutral, impassive, indifferent, pococurante (my personal favorite), uninterested, languid, perfunctory, undemonstrative, unfeeling, insouciant, listless, unsympathetic, emotionless, uncaring, lackadaisical, unresponsive, uneager, apathetic, casual, complacent, disinterested, unemotional, incurious, insensible, nonchalant, unconcerned, uncurious, unruffled, blase, phlegmatic, and Laodicean (so proud of myself for remembering that word lol).

Flat? Frigid?

Faint, flat, fruitless?

The best word for this is "indifferently".

if not frigid (fem.) insensitive.