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

Problem

ƒ(x)=x3+x

Solution

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

ƒ*(−x)=(−x)3+(−x)

2. Simplify the expression by applying the properties of odd powers.

ƒ*(−x)=−x3−x

3. Factor out a negative sign to compare the result to the original function ƒ(x)

ƒ*(−x)=−(x3+x)

4. Identify the relationship between ƒ*(−x) and ƒ(x)

ƒ*(−x)=−ƒ(x)

5. Conclude based on the definition of an odd function, which states that if ƒ*(−x)=−ƒ(x) the function is odd.

Final Answer

ƒ(x)=Odd

Want more problems? Check here!