Final answer:
The correct word to use is 'whoever' because it is the subject of the verb in the relative clause.
Step-by-step explanation:
In the sentence "The minister grimaced at whoever/whomever she greeted," the correct choice is "whoever." The use of "whoever" is based on its function as the subject of the verb "greeted" within the relative clause. To determine the appropriate pronoun, a helpful strategy involves reversing the clause and checking whether "he" or "she" can replace the relative pronoun.
If we rephrase the clause as "she greeted whoever," we can substitute "whoever" with "he" or "she." In this case, "she greeted he" is grammatically correct, while "she greeted him" would be incorrect. Therefore, the subjective form "whoever" is the appropriate choice in the original sentence.
Conversely, if the clause were "whomever she greeted," the substitution test would yield "she greeted him," making "whomever" the correct choice if the objective case were required.
This distinction illustrates the importance of identifying the pronoun's role within the clause – whether it serves as the subject or object of the verb. In this instance, the subject position is filled by "whoever," aligning with the minister being the one performing the greeting. Thus, "The minister grimaced at whoever she greeted" accurately reflects the intended meaning, highlighting the nuanced usage of relative pronouns in English grammar.