〜かどうか
whether (or not)
Plain form / Noun + かどうか
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かどうか turns a yes/no question into part of a sentence: 明日行けるかどうか分かりません, "I don't know whether I can go tomorrow". It's literally "whether … or how".
It follows plain forms; nouns and な-adjectives take it directly, without だ: 本当かどうか, "whether it's true".
It usually goes with verbs of knowing, asking and deciding: 分かる, 知る, 聞く, 決める, 確かめる.
For questions with a question word (who, what, when), you just use か, the next point: 誰が来るか分からない.
In speech, かどうか is often cut to just か (行けるか分からない), but the full form is clearer, and it's the one you'll see in writing.
Examples
明日行けるかどうか分かりません。
I don't know whether I can go tomorrow.
この話が本当かどうか知りません。
I don't know if this story is true.
おいしいかどうか、食べてみます。
I'll try it and see whether it's any good.
田中さんが来るかどうか聞いてください。
Please ask whether Tanaka's coming.
行くかどうか、まだ決めていません。
I haven't decided yet whether to go.