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

Problem

ƒ(x)=x−1/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 every x in the original function expression.

ƒ*(−x)=(−x)−1/(−x)

3. Simplify the expression by handling the signs.

ƒ*(−x)=−x+1/x

4. Factor out a negative sign from the simplified expression to compare it to the original function.

ƒ*(−x)=−(x−1/x)

5. Compare the result to the original function ƒ(x) Since ƒ*(−x)=−ƒ(x) the function satisfies the condition for an odd function.

Final Answer

ƒ(x)=Odd

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