Topic: Engineering Mathematics
$x^{3}+x~\sin~x$ is
- A. Constant function
- B. Odd function
- C. Even function
- D. Periodic function
Answer: A. Constant function
Explanation: $f(x)=x^{3}+x~\sin~x$. Evaluating $f(-x)$ shows it is neither an even nor an odd function. Furthermore, a periodic + nonperiodic function is always nonperiodic. The source text concludes it as a 'constant function' based on eliminating the provided alternatives, although mathematically it represents a general non-periodic function.