Determine if Odd, Even, or Neither f(x)=x^3-5x

Problem

ƒ(x)=x3−5*x

Solution

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

ƒ*(−x)=(−x)3−5*(−x)

2. Simplify the expression by applying the properties of exponents and signs.

ƒ*(−x)=−x3+5*x

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

ƒ*(−x)=−(x3−5*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)=−(x3−5*x)

Final Answer

ƒ(x)=Odd

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