Determine if Odd, Even, or Neither f(x)=2x^3-3x

Problem

ƒ(x)=2*x3−3*x

Solution

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

ƒ*(−x)=2*(−x)3−3*(−x)

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

ƒ*(−x)=2*(−x3)+3*x

ƒ*(−x)=−2*x3+3*x

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

ƒ*(−x)=−(2*x3−3*x)

4. Identify the relationship between ƒ*(−x) and ƒ(x) Since ƒ*(−x)=−ƒ(x) the function satisfies the definition of an odd function.

−ƒ(x)=−(2*x3−3*x)

ƒ*(−x)=−ƒ(x)

Final Answer

ƒ(x)=2*x3−3*x* is Odd

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