The given function is even.
Solution:
Given function:
[tex]f(x)=x^{6}-x^{4}[/tex]
If f(-x) = -f(x), then the function is odd.
If f(-x) = f(x), then the function is even.
[tex]f(x)=x^{6}-x^{4}[/tex]
Substitute x = -x
[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]
[tex]=x^{6}-x^{4}[/tex]
= f(x) (given)
f(-x) = f(x)
From the definition, it is even.
Hence the given function is even.
