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

Problem

ƒ(x)=x2−4

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 into the function for every instance of x

ƒ*(−x)=(−x)2−4

3. Simplify the expression by squaring the negative term. Since (−x)2=x2 the expression becomes:

ƒ*(−x)=x2−4

4. Compare the result to the original function ƒ(x) Since x2−4 is identical to the original ƒ(x) the condition ƒ*(−x)=ƒ(x) is satisfied.

Final Answer

ƒ(x)=x2−4* is Even

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