The infinitive phrase 'to find the perfect birthday gift' in the sentence serves as the subject.
The infinitive phrase 'to find the perfect birthday gift' in the sentence 'To find the perfect birthday gift is difficult' plays the role of a subject. It is the subject of the sentence describing what the action is about.
It functions as a nominal infinitive phrase, acting as the primary subject and governing the verb 'is difficult.'
Therefore, in this sentence, the infinitive phrase 'to find the perfect birthday gift' serves as the subject.
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