Determine if Odd, Even, or Neither f(x)=2x^4

Problem

ƒ(x)=2*x^4

Solution

1. Recall the definitions for function parity: 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)=2*(−x)^4

3. Simplify the expression by applying the power. Since the exponent 4 is even, (−x)^4=x^4

ƒ*(−x)=2*x^4

4. Compare the result to the original function. Since 2*x^4 is exactly ƒ(x) the condition for an even function is met.

ƒ*(−x)=ƒ(x)

Final Answer

ƒ(x)=2*x^4* is Even

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