Is 1 ( x ) 2 strictly greater than 1 x for all x?

Question

Is             1                        (          x          )                2             strictly greater than             1              x             for all x?

pressacvt · Accepted Answer

Step 1If       x    &amp;lt;    0   :When x is negative,             1      x       will be negative, but             1              x        2             will always be positive (because is       x    ∈    ℝ   , then             x      2        ≥    0   ). Therefore,             1              x        2             will be greater than             1      x       .If             1      x       :Both expressions will be undefined. Therefore, you can&#039;t compare them.If       0          &amp;lt;        x    &amp;lt;    1   :When x is between 0 and 1,             1              x        2             will be greater than             1      x       .If       x    =    1   :Both expressions will be equal (they will both be 1).If       x    &amp;gt;    1   :When x is greater than 1,             1      x       will be greater than             1              x        2             . This is because in             1      x       , you are dividing 1 by x only once, while in             1              x        2             , you are dividing 1 by x twice.

boloman0z · Accepted Answer

Step 1            1              x        2              ≤          1      x                    if              x    ≥    1  for example             1                        2          2                      =          1      4        &amp;lt;          1      2

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