Question

$f(x)=\left(\sin x^7\right)\cdot e^{x^5\mathrm{sgn}{x}^9}$ is

• A. an even function
• B. an odd function
• C. neither even nor odd
• D. None of these

Answer 1

Answer: (B)

$f(x)=\left(\sin x^7\right)e^{x^{5}sgn{x}^9}$
$\sin x^7\to$ odd, $sgn{x}^9\to$ odd, $x^5\to$ odd
$\therefore e^{x^{5}sgn{x}^9}\to$ even
$\therefore f(x)=$ odd $\times$ even $=$ odd