Question

Let $f(x)=\sqrt{\log _{6 / 5} \cos \{x\}}$ and $g(x)=\frac{2015 x(\tan \pi x-\sin \pi x)}{2\left[\frac{x}{\pi}+5\right]-9}$ is defined for all $x$ in domain of $f(x)$, then $g ( x )$ will be
[Note: [y] denotes greatest integer function and $\{y\}$ denotes fraction part function of $y$.]

• A. even function
• B. odd function
• C. both even and odd function
• D. neither even nor odd function

Answer 1

Answer: (C)

Domain of $f ( x ), \log _{6 / 5} \cos \{ x \} \geq 0 \Rightarrow \cos \{ x \} \geq 1 \Rightarrow \cos \{ x \}=1$
$\Rightarrow\{x\}=0 \Rightarrow x \in I$ and when $x \in I , g ( x )=0$ $\therefore g$ is both even and odd function