First slide

Functions (XII)

Question

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

Easy

A

2
B

1
C

-1
D

None of these

Solution

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

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