First slide

Functions (XII)

Question

$The function f (x) = (\tan x^{11}) e^{x^{5}} sgn (x^{11}) \cdot [\frac{1}{3 x^{2} + 2}], where [.] denotes greatest integer function, is$

Moderate

A

even function
B

odd function
C

even as well as odd function
D

neither even nor odd function

Solution

$x^{2} \geq 0 \Rightarrow 3 x^{2} \geq 0 \Rightarrow 3 x^{2} + 2 \geq 2$
$\Rightarrow \frac{1}{3 x^{2} + 2} \leq \frac{1}{2} \Rightarrow \frac{1}{3 x^{2} + 2} \in (0, \frac{1}{2}] \Rightarrow [\frac{1}{3 x^{2} + 2}] = 0 f o r a l l x \in R$
$\Rightarrow f (x) = 0$ $\Rightarrow f (- x) = 0 \Rightarrow f (- x) = f (x) a n d f (- x) = - f (x)$
$\Rightarrow f (x) i s e v e n a s w e l l a s o d d f u n c t i o n$

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