Questions: Determine algebraically whether the given function is even, odd, or neither. f(x)=2/x^(14) Is the given function even, odd, or neither? A. Even B. Odd C. Neither

Solution Steps

To determine if a function is even, odd, or neither, we check the symmetry properties:

1. A function $f(x)$ is even if $f(-x) = f(x)$ for all $x$.
2. A function $f(x)$ is odd if $f(-x) = -f(x)$ for all $x$.

For the given function $f(x) = \frac{2}{x^{14}}$, we will calculate $f(-x)$ and compare it to $f(x)$.

Given the function $f(x) = \frac{2}{x^{14}}$, we calculate $f(-x)$:

$$f(-x) = \frac{2}{(-x)^{14}}$$

Since $(-x)^{14} = x^{14}$ (because 14 is even), we have:

$$f(-x) = \frac{2}{x^{14}} = f(x)$$

Since $f(-x) = f(x)$, the function is even.

Final Answer