Question

How do you determine if `f(x) = x^2 / (x^4 + 1)` is an even or odd function?

Answer 1

f(x) is an even function

Explanation:

To determine if a function is even/odd consider the following.

• If f(x) = f( -x) , then f(x) is even

Even functions are symmetrical about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd

Odd functions have symmetry about the origin.

Test for even

`f(-x)=((-x)^2)/((-x)^4+1)=(x^2)/(x^4+1)`

Since f(x) = f( -x) , then f(x) is even

You could prove for yourself that f( -x) ≠ - f(x) and so f(x) is not odd.

Here is the graph of f(x). Note symmetry about y-axis.
graph{(x^2)/(x^4+1) [-10, 10, -5, 5]}