First slide

Functions (XII)

Question

If the real valued function $f (x) = \frac{a^{x} - 1}{x^{n} (a^{x} + 1)}$ is even, then n = ______

Easy

A

6
B

3
C

8
D

12

Solution

$f (- x) = f (x) \Rightarrow \frac{a^{- x} - 1}{{(- x)}^{n} (a^{- x} + 1)} = \frac{a^{x} - 1}{x^{n} (a^{x} + 1)}$
$\Rightarrow \frac{- 1}{{(- 1)}^{n}} = 1 \Rightarrow n = 3$

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