The function is $\"f(x)=1+3x^2-x^4\"$ .

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 $\"f(x)=1+3x^2-x^4\"$ .

$\"f(-x)=1+3(-x)^2-(-x)^4\"$

$\"f(-x)=1+3x^2-x^4\"$

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

Since $\"f(-x)=f(x)\"$ , the function $\"f(x)=1+3x^2-x^4\"$ is an even function.

Graph :

Graph the function $\"f(x)=1+3x^2-x^4\"$ .

$\"\"$

Observe the above graph, it is symmetry with respect to $\"y-\"$ axis.

So the function is an even function.

The function $\"f(x)=1+3x^2-x^4\"$ is an even function.