Is $f(x) = \frac{3}{2x^{6}-5}$ an even function, odd function, or neither?

Enter "odd", "even", or "neither".
$$f(-x) = \frac{3}{2(-x)^{6}-5} = \frac{3}{2x^{6}-5} = f(x)$$Hence $f$ is $\boxed{\text{even}}.$
even
Level 1
Intermediate Algebra
Problem: Is $f(x) = \frac{3}{2x^{6}-5}$ an even function, odd function, or neither?

Enter "odd", "even", or "neither".
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine if the function $f(x) = \frac{3}{2x^{6}-5}$ is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ and $-f(x)$. 

First, calculate $f(-x)$:
1. Substitute $-x$ into the function: 
   $f(-x) = \frac{3}{2(-x)^{6}-5}$.
2. Since $(-x)^{6} = x^{6}$ (even power), we have:
   $f(-x) = \frac{3}{2x^{6}-5}$.

Next, compare $f(-x)$ with $f(x)$:
- We find that $f(-x) = f(x)$.

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

Thus, the reasoning leads to the conclusion that the function $f(x)$ is classified as even.<|END_OF_LATENT|> The final answer is $even$.