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Algebra 2SuperchallengeFunctions, Relations & Transformations

Functions, Relations & Transformations · Superchallenge problem

Let f(x)=x2x2+(1−x)2f(x) = \dfrac{x^2}{x^2 + (1 - x)^2}. Find

f ⁣(1101)+f ⁣(2101)+f ⁣(3101)+⋯+f ⁣(100101).f\!\left(\tfrac{1}{101}\right) + f\!\left(\tfrac{2}{101}\right) + f\!\left(\tfrac{3}{101}\right) + \cdots + f\!\left(\tfrac{100}{101}\right).