Question

If f(x) + f(1-x) = 10 then the value of $f\left(\frac{1}{10}\right)+f\left(\frac{2}{10}\right)+.........+f\left(\frac{9}{10}\right)$

• A. is 45
• B. is 50
• C. is 90
• D. Cannot be determined

Answer 1

The correct option is A is 45

$f\left(\frac{1}{10}\right)+f\left(\frac{2}{10}\right)+f\left(\frac{3}{10}\right)+f\left(\frac{4}{10}\right)+f\left(\frac{5}{10}\right)+f\left(\frac{6}{10}\right)+f\left(\frac{7}{10}\right)+f\left(\frac{8}{10}\right)+f\left(\frac{9}{10}\right)$
$=\left[f\right(\frac{1}{10})+f(\frac{9}{10}\left)\right]+\left[f\right(\frac{2}{10})++f(\frac{8}{10}\left)\right]+\left[f\right(\frac{3}{10})++f(\frac{7}{10}\left)\right]+\left[f\right(\frac{4}{10})+f(\frac{6}{10}\left)\right]+f\left(\frac{5}{10}\right)]$
$=10+10+10+10+5=45$