Problem

Determine whether the function f(x)=x3+2x is odd, even, or neither.

Answer

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Answer

To check if the function is odd, we compute −f(x) and compare it to f(−x). −f(x)=−(x3+2x)=−x3−2x, which is equal to f(−x). So, the function is odd.

Steps

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)=−x3−2x, 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)=−(x3+2x)=−x3−2x, which is equal to f(−x). So, the function is odd.

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