unbounded function f(x)

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Not possessing both an upper and a lower bound. So for all positive real values V there is a value of the independent variable x for which |f(x)|>V. For example, f (x)=x2 is unbounded because f (x)≥0 but f(x) → ∞ as x → ±∞, i.e. it is bounded below but not above, while f(x)=x3 has neither upper nor lower bound.

Subjects: Mathematics.

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