To determine algebraically whether a function is even, substitute
-x into the and simplify. If the resulting is equal to
f(x), then the function is even; otherwise, it is not. For example, consider the following function.
f(x)=3x4−2x2+1
Substitute
-x for
x and simplify.
f(x)=3x4−2x2+1
f(-x)=3(-x)4−2(-x)2+1
f(-x)=3x4−2(-x)2+1
f(-x)=3x4−2x2+1
f(-x)=f(x)
Since
f(-x)=f(x), the given function is even.