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

Problem

ƒ(x)=cos(x)

Solution

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

2. Substitute −x into the function for every instance of x

ƒ*(−x)=cos(−x)

3. Apply the cosine parity identity, which states that cos(−θ)=cos(θ) for all θ

ƒ*(−x)=cos(x)

4. Compare the result to the original function. Since ƒ*(−x)=ƒ(x) the function is even.

Final Answer

ƒ(x)=cos(x)* is Even

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