Brain works 2

Algebra Level 2

f(1999)+f(2999)+f(3999)++f(998999)f\left(\frac1{999}\right) + f\left(\frac2{999}\right)+f\left(\frac3{999}\right)+ \cdots + f\left(\frac{998}{999}\right)

If f(x)=1f(1x)f(x) = 1 -f(1-x) for all real xx, evaluate the expression above.

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