how can you tell what an even or odd function is?

Question

anonymous · Answer

if f(x) =f(-x) ==> the function is even , and if f(-x) = -f(x) ===> the function is odd.

anonymous · Answer

so... how do you find if $$f(x)=x ^{4}-20x ^{2}$$ is even or odd?

anonymous · Answer

f(x) = x^4-20x^2 , f(-x) = (-x)^4 -20(-x)^2 = x^4=20x^2 ===> f(x) = f(-x) ==> f(x) is even

anonymous · Answer

thank you.

anonymous · Answer

the find -f(x) = -x^4+20x^2 ===> f(-x) is not wequal to -f(x) ===> f(x) is not odd

anonymous · Answer

check out this video: http://www.youtube.com/watch?v=2kPSG3dCmYo might help u

anonymous · Answer

f(x) = $$(-x)^{4}-20(-x)^{4}$$

So because the x is to the fourth power (and square), it reverts back to x. Like, $$(-x)^2 = x^2,$$ right? And $$(-x)^4 = x^4$$, right? And so on. However, $$(-x)^3$$ will just be $$(-x)^3$$, right? 

So in your case, the equation (after substituting in -x for x) will just "revert" back to f(x) =$$ x^4 - 20x^2$$, which is the same thing as your original function, therefore, your function is even.