nonplussed
Perplexed, not unfazed.
Nonplussed means perplexed or bewildered: The new rule left the staff nonplussed. A common error is to use nonplussed to mean calm or unbothered, as in He seemed nonplussed by the bad news and kept working. For calmness, use unfazed or unperturbed: He seemed unfazed by the bad news. The loose sense reverses the meaning of the word.
Examples
UseThe clerk was nonplussed by the missing page. (perplexed)
AvoidHe stayed nonplussed during the outage. (if you mean unfazed)
Dictionaries now also list nonplussed meaning “unfazed.” However, many people still consider this use an error, and they judge the speaker who uses nonplussed this way.