Determine if Odd, Even, or Neither f(x)=x^3+7

Problem

ƒ(x)=x3+7

Solution

1. Substitute −x for x in the function to find ƒ*(−x)

ƒ*(−x)=(−x)3+7

2. Simplify the expression by applying the power to the negative variable.

ƒ*(−x)=−x3+7

3. Compare ƒ*(−x) to the original function ƒ(x)

ƒ*(−x)≠ƒ(x)

−x3+7≠x3+7

The function is not even.

4. Compare ƒ*(−x) to the negative of the original function −ƒ(x)

−ƒ(x)=−(x3+7)

−ƒ(x)=−x3−7

ƒ*(−x)≠−ƒ(x)

−x3+7≠−x3−7

The function is not odd.

5. Conclude that since the function satisfies neither the even condition ƒ*(−x)=ƒ(x) nor the odd condition ƒ*(−x)=−ƒ(x) it is neither.

Final Answer

ƒ(x)=x3+7* is Neither

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