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An increasing function in mathematics is a function where, for any two points ( x_1 ) and ( x_2 ) in its domain, if ( x_1 < x_2 ), then ( f(x_1) < f(x_2) ). This means that as the input values increase, the output values also increase. A function can be strictly increasing, where the inequality is strict, or non-decreasing, where it allows for equal output values. Increasing functions are important in various mathematical analyses and applications.

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