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

Problem

ƒ(x)=ex

Solution

1. Recall the definitions of even and odd functions. A function is even if ƒ*(−x)=ƒ(x) and odd if ƒ*(−x)=−ƒ(x)

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

ƒ*(−x)=e(−x)

3. Compare ƒ*(−x) with ƒ(x) Since e(−x)=1/(ex) it is clear that e(−x)≠ex for all x≠0 Therefore, the function is not even.

4. Compare ƒ*(−x) with −ƒ(x) Since −ƒ(x)=−ex it is clear that e(−x)≠−ex for all x Therefore, the function is not odd.

5. Conclude that because the function satisfies neither condition, it is neither even nor odd.

Final Answer

ƒ(x)=ex* is neither even nor odd

Want more problems? Check here!