Parity of Functions

Solution Approach: We need to compute $f(-x)$ and compare it with $f(x)$.

Detailed Steps:

1. Compute $f(-x)$: $f(-x) = (-x)^3 + (-x) = -x^3 - x = -(x^3 + x) = -f(x)$
2. Comparison: Since $f(-x) = -f(x)$, this function is an odd function.

Answer: This function is an odd function.

Solution Approach: We need to compute $f(-x)$ and compare it with $f(x)$.

Detailed Steps:

1. Compute $f(-x)$: $f(-x) = (-x)^2 + 2(-x) + 1 = x^2 - 2x + 1$
2. Comparison: $f(-x) \neq f(x)$ and $f(-x) \neq -f(x)$
3. Therefore this function is neither odd nor even.

Answer: This function is neither odd nor even.