I've read a lot of mangas and I've noticed the use of がいい after a verb e.g.
Does it work as an adverb?
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No, 見る and 諦めた方 are grammatically subjects, not adverbs in those sentences. Words marked with が should be nouns, of course.
As you know,
noun + がいい (lit. "～ is good", with exhaustive-listing ga) is usually used when you choose one thing from a few possible options.
If you want to use this with two or more possible actions (verbs), you normally need a nominalizer, which can turn verbs into nouns:
Alternatively, you can use 方【ほう】, which is a noun. ほう literally means something like "side", but it has many usages, including comparing two or more options. See: What is 方 used for (when attached to a た-verb)? and This usage of 方 confuses me
- 本を書くほうがいい。 I like writing books (rather than doing something else). / You should write a book about it.
- ラーメンのほうがいい。 （≒ラーメンがいい）
What I've explained so far is about modern, standard Japanese grammar. However,
dictionary-form + がいい existed in classic Japanese, and is still in use in some rare cases. This is one way of giving an order. (To be precise, this verb form is 連体形, which was slightly different from the dictionary form in classic Japanese) See: <動詞の辞書形> + がよい ― How is this allowed?
- 見るがいい！ (≒"Behold!")
Note that this is a very pompous way of speaking, and no one speak like this in real life. In manga, you would typically see this used by a noble princess, old man, etc.
The negative counterpart is perhaps
dictionary-form + でない. See: 何も言うでない ! meaning and origin
見るがいい。means "Why don't you take a look at it?"
見たほうがいい。means "You'd better take a look at it."
諦めるがいい。means "Just give up on it."
諦めたほうがいい。 means "You'd better give up on it."