آنها پرسیدند که آیا تابع این متغیر را برمی‌گرداند یا خیر.

Questions & Answers about آنها پرسیدند که آیا تابع این متغیر را برمی‌گرداند یا خیر.

Why does the sentence end with یا خیر instead of the more common یا نه for 'or not'?
خیر is a highly formal version of نه (no). Because this sentence discusses technical concepts like a function (تابع) and a variable (متغیر), it has an academic or professional tone. In such formal contexts, appending یا خیر to a reported yes/no question is much more natural and expected than the conversational یا نه.
Is it strictly necessary to use که آیا together, or could I just use آیا to mean 'whether'?
You can definitely just drop که and use آیا. The که acts as a conjunction connecting the main verb (پرسیدند) to the reported question, similar to saying 'They asked that whether...' in older English. While که is often dropped in spoken Farsi, keeping که آیا together is standard in formal writing and makes the boundary between the clauses very clear.
I know the verb for 'to return' is برگشتن. Why is برمی‌گرداند used here instead?
برگشتن is intransitive, meaning the subject itself goes back. Here, the function is returning something else (the variable). For this, you need the transitive verb برگرداندن (to return something or give something back), which takes the direct object marker را after این متغیر.
Can I use تابع for any kind of 'function', like the function of a tool or a committee?
No, تابع is highly specific to mathematics and computer programming. If you want to talk about the function, purpose, or performance of a machine or a group in everyday situations, you would use a word like عملکرد instead.

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