Question

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

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

Answer 1

The correct option is B $50$

Clearly required expression contains 10 terms which can be grouped into 5 pairs each having complementary arguments which add up to 1.

Answer $=f\left(\frac{1}{10}\right)$ +$f\left(\frac{9}{10}\right)$+$f\left(\frac{2}{10}\right)$ +$f\left(\frac{8}{10}\right)$+..............................

$=f\left(\frac{1}{10}\right)$+$f(1-\frac{1}{10})$ +$f\left(\frac{2}{10}\right)$ +$f(1-\frac{2}{10})$ +...............................

The first condition of the statement hence gives us the value to be $5\times 10=50$