Determine if Odd, Even, or Neither f(x)=cos(2x)

Problem

ƒ(x)=cos(2*x)

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 evaluate ƒ*(−x)

ƒ*(−x)=cos(2*(−x))

3. Simplify the expression inside the cosine function.

ƒ*(−x)=cos(−2*x)

4. Apply the even property of the cosine function, which states that cos(−θ)=cos(θ) for any angle θ

cos(−2*x)=cos(2*x)

5. Compare the result to the original function. Since ƒ*(−x)=cos(2*x) and ƒ(x)=cos(2*x) we see that ƒ*(−x)=ƒ(x)

ƒ*(−x)=ƒ(x)

Final Answer

ƒ(x)=cos(2*x)* is Even

Want more problems? Check here!