Determine whether the function f(x)=2x-x^(5) is even, odd or neither. neither even odd

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Determine whether the function  f(x)=2x-x^(5) is even, odd or neither. neither even odd

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Define function f(x): Define the function f(x). The given function is f(x)=2x-x^(5). We need to determine if this function is even, odd, or neither by checking the symmetry properties.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) = 2(-x) - (-x)^(5) f(-x) = -2x - (-x)^5Simplify f(-x): Simplify f(-x). Simplify the expression for f(-x) by evaluating the exponents. f(-x) = -2x - (-1)^5 * x^5 f(-x) = -2x + x^5Compare f(x) and f(-x): Compare f(x) and f(-x). We have the original function f(x) = 2x - x^5 and the transformed function f(-x) = -2x + x^5. Since f(x) ≠ f(-x), 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) = -2x + x^5 from Step 3. Now, calculate -f(x) by multiplying the original function by -1. -f(x) = -(2x - x^5) -f(x) = -2x + x^5Compare f(-x) and -f(x): Compare f(-x) and -f(x). We have f(-x) = -2x + x^5 from Step 3 and -f(x) = -2x + x^5 from Step 5. Since f(-x) = -f(x), the function is odd.

Determine whether the function $f(x)=2 x-x^{5}$ is even, odd or neither. $\newline$ neither $\newline$ even $\newline$ odd

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Determine whether the function f(x)=2x−x5 f(x)=2 x-x^{5} f(x)=2x−x5 is even, odd or neither.\newlineneither\newlineeven\newlineodd

Determine whether the function $f(x)=2 x-x^{5}$ is even, odd or neither. $\newline$ neither $\newline$ even $\newline$ odd