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Determine if the conjecture is true or false. If true, explain your reasoning briefly. If false provide a counterexample.
A. Given that 1/5[tex]\leq[/tex]5,
1/20[tex]\leq[/tex], 20,
and 1/38[tex]\leq[/tex]38, you conjecture that 1/x[tex]\leq[/tex]x all real numbers x[tex]\leq[/tex] 0

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sqdancefan

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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

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