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anemone
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Given that $(x+1)f(x^2+7x+10)+\left(\dfrac{1-x}{4x}\right)f(x^2+11x+24)=\dfrac{100(x^2+4)}{x}$, find $f(2)+f(3)+\cdots+f(400)$.
A functional equation is an equation that involves functions rather than just variables. It involves finding the relationship between two or more functions.
The sum of solutions to a functional equation refers to the total value of all possible solutions that satisfy the given equation.
The process of finding the sum of solutions to a functional equation involves solving the equation for all possible values of the variables, and then adding up all the solutions to get the final sum.
Yes, there are various strategies and methods that can be used to find the sum of solutions to a functional equation. Some common methods include substitution, elimination, and graphing.
Yes, depending on the given equation, the sum of solutions can have multiple values. This can occur when the equation has multiple solutions or when there are multiple ways to express the solutions.