Question

If f(x) = 1 - f(1 - x), then the value of $f\left(\frac{1}{999}\right)+f\left(\frac{2}{999}\right)+......+f\left(\frac{998}{999}\right)$ is

• A. 998
• B. 1
• C. 499
• D. None of these

Answer 1

The correct option is C 499

$f\left(x\right)=1-f(1-x)\Rightarrow f\left(x\right)+f(1-x)=1Now,f\left(\frac{1}{999}\right)+f\left(\frac{2}{999}\right)+...f\left(\frac{997}{999}\right)+f\left(\frac{998}{999}\right)=\left[f\right(\frac{1}{999})+f(\frac{998}{999}\left)\right]+\left[f\right(\frac{2}{999})+f(\frac{997}{999}\left)\right]+......=\left[f\right(\frac{1}{999})+f(1-\frac{1}{999}\left)\right)]+[f\left(\frac{2}{999}\right)+f(1-\frac{2}{999})]+....=1+1+1+....499times=499$