Answer :
The function f(x)=-x^(4)-7x^(6)+2x^(2) can be classified as neither even nor odd.
To determine if a function is even or odd, we need to check if it satisfies the properties of symmetry.
1. Even function: A function f(x) is even if f(x) = f(-x) for all values of x. In other words, if we replace x with -x in the function and the result is the same, then the function is even.
2. Odd function: A function f(x) is odd if f(x) = -f(-x) for all values of x. In other words, if we replace x with -x in the function and the result is the negative of the original function, then the function is odd.
Let's apply these properties to the given function:
f(x) = -x^(4) - 7x^(6) + 2x^(2)
1. Replacing x with -x, we get:
f(-x) = -(-x)^(4) - 7(-x)^(6) + 2(-x)^(2)
= -x^(4) - 7x^(6) + 2x^(2)
Since f(x) = f(-x), the function satisfies the condition for an even function.
2. Replacing x with -x, we get:
-f(-x) = -(-x^(4) - 7(-x)^(6) + 2(-x)^(2))
= x^(4) + 7x^(6) - 2x^(2)
Since -f(-x) is not equal to the original function f(x), the function does not satisfy the condition for an odd function.
Therefore, the function f(x)=-x^(4)-7x^(6)+2x^(2) is neither even nor odd.
Learn more about symmetry
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