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