A functionis one-to-one if for everyandin the domain,implies. To verify this, assume. Simplify the equation to find that. Therefore, the functionis.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the understanding of the definition of a one-to-one function by verifying that different inputs produce different outputs.
Key Concept Explanation
A function is one-to-one if each element in the domain maps to a unique element in the range. Mathematically, if , then .
Step-by-step Solution
1. Assume :
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