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No.

For example, y = 7 is monotonic. It may be a degenerate case, but that does not disallow it. It is not a bijection unless the domain and range are sets with cardinality 1.

Even a function that is strictly monotonic need not be a bijection. For example, y = sqrt(x) is strictly monotonic [increasing] for all non-negative x. But it is not a bijection from the set of real numbers to the set of real numbers because it is not defined for negative x.

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Q: Is a monotonic function a bijection?
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