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Non-Distributive Property of Function Evaluation
A common misconception when working with function notation is assuming that a function distributes over addition, similar to the distributive property of multiplication. However, for a general mathematical function , the evaluation of a sum is not necessarily equal to the sum of the evaluated functions. Mathematically, this means that . This non-distributive property emphasizes that the function name cannot simply be distributed across terms inside the parentheses. Instead, the entire expression inside the parentheses must be substituted for the independent variable before simplifying.
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Non-Distributive Property of Function Evaluation