Topic: Engineering Mathematics
$x^{3}+x \sin x$ is a ... function
- A. Constant function
- B. Odd function
- C. Even function
- D. Periodic function
Explanation: Let $F(x) = x^{3}+x \sin x$. $F(-x) = (-x)^{3}+(-x)\sin(-x) = -x^{3}+x \sin x$. It does not equal $F(x)$ (not even) and does not equal $-F(x)$ (not odd). It is not constant, nor is it periodic due to the $x^{3}$ term. Hence, none of the options given are correct.