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

Problem

ƒ(x)=x/(x^2−1)

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 every instance of x in the original function.

ƒ*(−x)=(−x)/((−x)^2−1)

3. Simplify the expression by squaring the negative term in the denominator.

ƒ*(−x)=(−x)/(x^2−1)

4. Factor out the negative sign from the numerator to compare it to the original function.

ƒ*(−x)=−x/(x^2−1)

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

Final Answer

ƒ(x)=Odd

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