Question

Determine if the conjecture is true or false. If true, explain your reasoning briefly. If false provide a counterexample.

Answer 1

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Answer:

  false

Step-by-step explanation:

The conjecture shown in this problem statement does not follow from the examples offered. They support the notion that ...

  1/x ≤ x . . . . for x ≥ 0 (not x ≤ 0)

There are several possible counterexamples showing the conjecture is FALSE.

1. 1/0 is undefined
2. 1/(-5) > -5 . . . . . . . . a case for x < 0

If the intended domain is x ≥ 0, then the conjecture can also be demonstrated to be false for 0 < x < 1:

1. 1/(1/5) > 1/5