Determine whether the function f(x)=-3-x^(4)+7x is even, odd or neither. odd neither even

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Determine whether the function  f(x)=-3-x^(4)+7x is even, odd or neither. odd neither even

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Define function f(x): Define the function f(x). The given function is f(x)=-3-x^(4)+7x. We need to determine if this function is even, odd, or neither.Check even function: Check if the function is even. An even function satisfies the condition f(x) = f(-x) for all x in the domain. Calculate f(-x) by substituting -x for x in the function f(x). f(-x) = -3-(-x)^(4)+7(-x) f(-x) = -3-x^(4)-7xCompare f(x) and f(-x): Compare f(x) and f(-x). We have f(x) = -3-x^(4)+7x and f(-x) = -3-x^(4)-7x. Since f(-x) is not equal to f(x) (because of the opposite signs in front of the 7x term), the function is not even.Check odd function: Check if the function is odd. An odd function satisfies the condition f(-x) = -f(x) for all x in the domain. We already have f(-x) = -3-x^(4)-7x. Now we need to check if this is equal to -f(x). -f(x) = -(-3-x^(4)+7x) -f(x) = 3+x^(4)-7xCompare f(-x) and -f(x): Compare f(-x) and -f(x). We have f(-x) = -3-x^(4)-7x and -f(x) = 3+x^(4)-7x. Since f(-x) is not equal to -f(x) (because the constant terms do not cancel out and the signs of the x^(4) terms are different), the function is not odd.Conclude function type: Conclude whether the function is even, odd, or neither. Since the function f(x) does not satisfy the conditions for being even or odd, we conclude that the function is neither even nor odd.

Determine whether the function $f(x)=-3-x^{4}+7 x$ is even, odd or neither. $\newline$ odd $\newline$ neither $\newline$ even

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Determine whether the function $f(x)=-3-x^{4}+7 x$ is even, odd or neither. $\newline$ odd $\newline$ neither $\newline$ even