First slide

Algebra of real valued functions

Question

If $f (x) = \frac{9^{x}}{9^{x} + 3}$ then
$f (\frac{1}{1996}) + f (\frac{2}{1996}) + ...... + f (\frac{1995}{1996}) =_____$

Moderate

A

996.5
B

997.5
C

998.5
D

999.5

Solution

$f (x) + f (1 - x) = \frac{9^{x}}{9^{x} + 3} + \frac{9^{1 - x}}{9^{1 - x} + 3} = 1$

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