Determine if Odd, Even, or Neither f(x)=-9x^3+8x

Problem

ƒ(x)=−9*x3+8*x

Solution

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

ƒ*(−x)=−9*(−x)3+8*(−x)

2. Simplify the expression by applying the properties of exponents, noting that (−x)3=−x3

ƒ*(−x)=−9*(−x3)−8*x

ƒ*(−x)=9*x3−8*x

3. Factor out a negative sign from the simplified expression to compare it to the original function.

ƒ*(−x)=−(−9*x3+8*x)

4. Compare the result to the original function ƒ(x) Since ƒ*(−x)=−ƒ(x) the function satisfies the definition of an odd function.

−ƒ(x)=−(−9*x3+8*x)=9*x3−8*x

ƒ*(−x)=−ƒ(x)

Final Answer

ƒ(x)=Odd

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