Is the function given by y=-x^4+2x^2-1 odd even or neither, dumb it down for me as how you find the answer please

Question

anonymous · Answer

A function f(x) is even if
$$f(-x)=f(x)$$
And it is odd if
$$f(-x)=-f(x)$$
Now, substitute x in your function with -x and see how it works out:
$$f(x)=-x^4+2x^2-1$$
then
$$f(-x)=-(-x)^4+2(-x)^2-1$$
You know that -x = -1*x, and that -1 raised to an EVEN power will always be positive 1.
So,
$$f(-x)=-(-1*x)^4+2(-1*x)^2-1$$
$$f(-x)=-1*(x)^4+2*1(x)^2-1$$
$$f(-x)=-x^4+2x^2-1$$
Therefore
$$f(-x)=f(x)$$
Which means that the function is even.

anonymous · Answer

Thank you, really helpful exactly what I needed