If f(x) = 1 - f(1 - x), then the value of f(1999)+f(2999)+......+f(998999) is
A
998
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B
1
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C
499
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D
None of these
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Solution
The correct option is C 499 f(x)=1−f(1−x)⇒f(x)+f(1−x)=1Now,f(1999)+f(2999)+...f(997999)+f(998999)=[f(1999)+f(998999)]+[f(2999)+f(997999)]+......=[f(1999)+f(1−1999))]+[f(2999)+f(1−2999)]+....=1+1+1+....499times=499