Problem

Determine whether the function \(f(x) = x^3 + 2x\) is odd, even, or neither.

Solution

Step 1 :An even function is a function that satisfies \(f(x) = f(-x)\) for all x in the domain of f.

Step 2 :An odd function is a function that satisfies \(f(x) = -f(-x)\) for all x in the domain of f.

Step 3 :To check if the function is even, we compute \(f(-x)\) and compare it to \(f(x)\). \(f(-x) = (-x)^3 + 2(-x) = -x^3 - 2x\), which is not equal to \(f(x)\). So, the function is not even.

Step 4 :To check if the function is odd, we compute \(-f(x)\) and compare it to \(f(-x)\). \(-f(x) = -(x^3 + 2x) = -x^3 - 2x\), which is equal to \(f(-x)\). So, the function is odd.

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Source: https://solvelyapp.com/problems/EPjyEn6dhD/

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