Both "I hope you are doing good" and "I hope you are doing well" are commonly used expressions in informal English, and they are generally interchangeable in most situations. However, there is a subtle difference in their meanings and grammatical correctness.
"I hope you are doing good" is more colloquial and often used in casual speech. "Good" in this context is an adjective describing a state of being or condition. It implies that you are wishing the person is in a positive or favorable state or feeling emotionally good.
"I hope you are doing well" is more formal and grammatically correct. "Well" in this context is an adverb describing the manner or way in which someone is doing. It implies that you are wishing the person is in good health, spirits, or overall well-being.
From a strict grammatical standpoint, "I hope you are doing well" is considered more accurate because "well" is an adverb that modifies the verb "doing." However, as mentioned earlier, both versions are widely used, and in casual conversation, people often use them interchangeably without any significant issues.
So, if you want to be strictly grammatically correct, it's better to use "I hope you are doing well." If you are in a relaxed, informal setting, "I hope you are doing good" would be perfectly acceptable.