Determine if Odd, Even, or Neither f(x)=1/(x^2)

Problem

ƒ(x)=1/(x2)

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)=1/((−x)2)

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

ƒ*(−x)=1/(x2)

4. Compare the result to the original function. Since ƒ*(−x)=1/(x2) and ƒ(x)=1/(x2) it follows that ƒ*(−x)=ƒ(x)

5. Conclude that the function satisfies the condition for an even function.

Final Answer

ƒ(x)=1/(x2)* is Even

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