How do you determine if # f(x) = x^2 / (x^4 + 1)# is an even or odd function?
1 Answer
May 18, 2016
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]}
