also the copula هو since the predicate, المطبخ, is definite. https://forum.duolingo.com/comment/33827406/%D8%B3%D8%A7%D9%85%D9%92%D9%8A%D8%A9-%D8%AC%D8%A7%D8%B1%D8%A9-%D8%AC%D9%8E%D8%AF%D9%8A%D8%AF%D8%A9 (see there the response of AmineHadji1)
Pretty similar with Arabic. The root for مطبخٌ - "maTbakhun" is طَبَخَ "Tabakha" - to cook (ط ب خ). We form the "maTbakhun" word from "Tabakha" with wazan/pattern maf3al (وزن مَفْعل) to indicate the place. Literally, maTbakh means: "the place to cook".
By the way,
I don't see any nikud at the last letter ח. So, is the last letter automatically regarded as a dead letter (ie. ח has no sound)? Whilst in Arabic, ACTUALLY there should be خٌ -khun at the last letter. مطبخٌ maTbakhun.
Secondly, how do you write the nikud in Android Phone, AniOhev? My Gboard doesn't provide the nikud, I have tried some nikud app but doesn't work well.
I think for Android Phone you just choose the Hebrew font, as with the i-phone, but I'm not positive so you can google how to do it. It may be easier on computer to download keyboard fonts. The last latter is a chet and it sounds more or less like a k. Yes, for מִטְבָּח the the chet ends the word.