Question

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

Answer 1

even function

Explanation:

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

• If a function is even then f(x) = f(-x) , for all x

Even functions are symmetrical about the y-axis

• If a function is odd then f(-x) = - f(x)

Odd functions have symmetry about the origin

Test for even :

`g(-x) = (4 + (-x)^2)/(1 + (-x)^4) = (4 + x^2)/(1 + x^4) = g(x)" hence even "`

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