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Replacement cost is the correct method to curb functional obsolescence in cost approaches. This method assesses the current cost to replace an asset with a similar new asset that serves the same purpose, without regard to the existing asset's depreciation or physical condition. By focusing on the cost to replicate the property, it allows for adjustments relevant to modern standards and technologies, thereby addressing issues of functional obsolescence—situations where the property is less desirable because it does not meet current market expectations or requirements.

The other methods mentioned do not specifically target functional obsolescence in the same way. Historical cost reflects the original cost of the property without accounting for current market conditions, and therefore may not adequately capture obsolescence. Fair market value involves assessing what a buyer would pay and does not specifically adjust for functional deficiencies. The comparative sales approach looks at recent sales of similar properties, which may not effectively isolate or address functionality issues within a specific property context. Thus, replacement cost stands out as a proactive method to mitigate the impacts of functional obsolescence in property valuation.