Determine whether the function f(x)=-7x^(4)-6x^(2)+2x^(6) is even, odd or neither. even odd neither

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Determine whether the function  f(x)=-7x^(4)-6x^(2)+2x^(6) is even, odd or neither. even odd neither

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Check Even Symmetry: To determine if the function is even, odd, or neither, we need to check the symmetry properties of the function. A function f(x) is even if f(-x) = f(x) for all x in the domain of f. A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. If neither condition is met, the function is neither even nor odd.Replace x with -x: First, we will check if the function is even. We do this by replacing x with -x in the function and simplifying. f(-x) = -7(-x)^(4) - 6(-x)^(2) + 2(-x)^(6)Simplify Expression: Now we simplify the expression by calculating the powers of -x. f(-x) = -7((-x)^(4)) - 6((-x)^(2)) + 2((-x)^(6)) Since the powers are all even, the negative signs will be canceled out. f(-x) = -7(x^(4)) - 6(x^(2)) + 2(x^(6))Compare to Original Function: We compare this expression to the original function f(x). f(-x) = -7(x^(4)) - 6(x^(2)) + 2(x^(6)) is the same as f(x) = -7x^(4) - 6x^(2) + 2x^(6). Since f(-x) = f(x), the function is even.

Determine whether the function $f(x)=-7 x^{4}-6 x^{2}+2 x^{6}$ is even, odd or neither. $\newline$ even $\newline$ odd $\newline$ neither

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Determine whether the function f(x)=−7x4−6x2+2x6 f(x)=-7 x^{4}-6 x^{2}+2 x^{6} f(x)=−7x4−6x2+2x6 is even, odd or neither.\newlineeven\newlineodd\newlineneither

Determine whether the function $f(x)=-7 x^{4}-6 x^{2}+2 x^{6}$ is even, odd or neither. $\newline$ even $\newline$ odd $\newline$ neither