Assume f: R R is a function. We say that f is increasing if *>y implies...

  

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Assume f: R→ R is a function. We say that f is increasing if *>y implies that f(x) > f(y), for any r, y R. Below are two conjectures. For each, either prove they are true or find a counterexample. (a) Conjecture 1: If f: R→ R is an increasing function, then f is injective. (b) Conjecture 2: If f: R→ R is an increasing function, then f is surjective. Assume f: R→ R is a function. We say that f is increasing if *>y implies that f(x) > f(y), for any r, y R. Below are two conjectures. For each, either prove they are true or find a counterexample. (a) Conjecture 1: If f: R→ R is an increasing function, then f is injective. (b) Conjecture 2: If f: R→ R is an increasing function, then f is surjective.

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ANSWER a Conjecture 1 If f R R is an increasing function then f is injective This conjecture is true ... View the full answer