Question

Prove algebraically what type of function this is (even, odd, or neither).

Answer 1

The given function is even.

Solution:

Given function:

$f(x)=x^{6}-x^{4}$

If f(-x) = -f(x), then the function is odd.

If f(-x) = f(x), then the function is even.

$f(x)=x^{6}-x^{4}$

Substitute x = -x

$f(-x)=(-x)^{6}-(-x)^{4}$

          $=x^{6}-x^{4}$

          = f(x)   (given)

   f(-x) = f(x)

From the definition, it is even.

Hence the given function is even.