Problem

Determine whether the function \(f(x) = x^4 - 2x^2 + 1\) is odd, even, or neither.

Answer

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Answer

We can see that \(f(x) = f(-x)\), so the function is even.

Steps

Step 1 ：An even function is one for which \(f(x) = f(-x)\), for all \(x\) in the function's domain. An odd function is one for which \(f(x) = -f(-x)\), for all \(x\) in the function's domain.

Step 2 ：For the given function, let's first find \(f(-x)\).

Step 3 ：\(f(-x) = (-x)^4 - 2(-x)^2 + 1 = x^4 - 2x^2 + 1\).

Step 4 ：We can see that \(f(x) = f(-x)\), so the function is even.

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