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Are the following statements true or false? In each case, prove your answer. There is a strictly...

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Advance Math

Are the following statements true or false? In each case, proveyour answer.

  1. There is a strictly decreasing function f fromN to N with f(0) = 100.
  2. Let f(x) and g(x) be strictly increasing functions fromR to R. Then (f + g)(x) is alsostrictly increasing.
  3. Once again, let f(x) and g(x) be strictly increasing functionsfrom R to R. Then (f×g)(x) isalso strictly increasing.

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