Examine if f(x)=x^3-(1/x) is even,odd or neither?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember what an odd function means, hence if `f(-x) = -f(x)` , the function is odd. You also need to remember what an even function means, hence if f(-x) = f(x), the function is even.

You need to test if the function is odd, even or neither, replacing `-x` for `x` in equation of the function, such that:

`f(-x) = (-x)^3 - 1/(-x) => f(-x) = -x^3 + 1/x`

You may factor out -`1` , such that:

`f(-x) = -(x^3 - 1/x)`

You need to notice that the expression `x^3 - 1/x` represents the equation of the function `f(x)` , hence, you may replace `f(x)` for `x^3 - 1/x` , such that:

`f(-x) = -f(x)`

Since `f(-x) = -f(x)` yields that the function is odd.

Hence, evaluating if the given function is odd, even or neither, yields that `f(-x) = -f(x)` , thus, the function is odd.

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