The 助動詞（じょどうし） (auxiliary verb)
べき, being the 連体形（れんたいけい） (attributive form) of べし, is a structure in Japanese that is often paired with verbs to express that something ‘ought to be done’. It implies some sort of moral obligation, or that (A) is the only reasonable course of action. This comes from the kanji 可（べ）き, which carries the meaning of being something ‘permissible’ (indicating that any other action would not be acceptable).
べき will be paired with the plain (non-past) form of a verb, before being followed by either
だ, or another noun.
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そういう事（こと）は本人（ほんにん）に言（い）うべきだ。
You ought to say things like that to the person themselves.
お客（きゃく）さんの意見（いけん）はちゃんと聞（き）くべきだ。
You ought to properly listen to customers' opinions.
ハマサキさんは尊敬（そんけい）するべき人（ひと）だ。
Hamasaki-san is someone you ought to look up to.
あなたに教（おし）えるべき事（こと）はこれで全部（ぜんぶ）です。
Of all the things I ought to teach you, this is the last one.
べき is also sometimes translated as ‘must do (A)’, or ‘should do (A)’ but it is important to remember that it will always have the nuance of being the only ‘permissible’ choice, and is therefore very strong.
It is important to note that the verb appearing with
べき cannot be in past tense, and you will need to use
だった or
でした after
べき, if you would like to say that something ‘ought to have been done’ in the past.
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やばいやばい、車（くるま）が止（と）まりそう！高速（こうそく）に乗（の）る前（まえ）にガソリンを入（い）れておくべきだった。
This is not good… ahhh not good, the car is about to stop! I should have filled the car up with gasoline before I got on the highway.
大変（たいへん）申（もう）し訳（わけ）ございません。こちらがもっと早（はや）く気（き）づくべきでした。
We are very sorry. We should have noticed this earlier.
In modern Japanese, there are only 18 助動詞（じょどうし） (auxiliary verbs), of which べき is not one. べし (the standard form) is considered to be 文語（ぶんご） (classical Japanese). Due to this, べき (and べし) are often referred to as 文語助動詞（ぶんごじょどうし） (classical auxiliary verbs).
The combination of
する and
べき is a rare grammatical exception in Japanese, in which two forms are both considered equally correct. Due to this, either するべき, or すべき may be used.
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結婚（けっこん）する前（まえ）に相手（あいて）と将来（しょうらい）の話（はな）しをするべきだ。
Before marrying, you should talk about the future with your partner.
家族（かぞく）は何（なに）があっても大切（たいせつ）にすべきだ。
You should prioritize family no matter what happens.