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Консультация № 121557
04.02.2008, 10:29
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Решите пожалуйста задачку по дискретной математике:
Дана функция f(x) = 2^x+sqrt(x), отображающая множество положительных действительных чисел во множество всех действительных чисел. Является ли эта функция сюръективной, инъективной, биективной? Почему?
Дана функция f(x) = 2^x+sqrt(x), отображающая множество положительных действительных чисел во множество всех действительных чисел. Является ли эта функция сюръективной, инъективной, биективной? Почему?
Обсуждение
Неизвестный
04.02.2008, 21:48
общий
это ответ
Здравствуйте, Sasha34!
для положительных х функция f(x) строго монотонно возрастает и принимает значения в интервале от 1 до бесконечности, что не является множеством всех действительных чисел .
Поэтому отображение не сюръективно и , поэтому, также не биективно
Поскольку f(x) строго монотонно возрастаюшая , то инъективной она является,
т.к. разным значениям х соответствуют разные значения f(x)
для положительных х функция f(x) строго монотонно возрастает и принимает значения в интервале от 1 до бесконечности, что не является множеством всех действительных чисел .
Поэтому отображение не сюръективно и , поэтому, также не биективно
Поскольку f(x) строго монотонно возрастаюшая , то инъективной она является,
т.к. разным значениям х соответствуют разные значения f(x)
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