The function is $\"f(x)=\\frac{x^2}{x^4+1}\"$ .

If $\"f(-x)=f(x)\"$ , then the function is said to be even.

If $\"f(-x)=-f(x)\"$ , then the function is said to be odd.

Substitute $\"x=-x\"$ in $\"f(x)=\\frac{x^2}{x^4+1}\"$ .

$\"f(-x)=\\frac{(-x)^2}{(-x)^4+1}\"$

$\"f(-x)=\\frac{x^2}{x^4+1}\"$

$\"f(-x)=f(x)\"$

Since $\"f(-x)=f(x)\"$ , the function $\"f(x)=\\frac{x^2}{x^4+1}\"$ is an even function.

Graph :

Graph the function $\"f(x)=\\frac{x^2}{x^4+1}\"$ .

$\"\"$

Observe the above graph :

It is symmetry with respect to the $\"y-\"$ axis.

So the function is an even function.

The function $\"f(x)=\\frac{x^2}{x^4+1}\"$ is an even function.