Question 1044462
.
the solution set of the inequality 1/x<=x is ?
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<pre>
1.  If x > 0, then the inequality {{{1/x}}} <= x is equivalent to {{{x^2}}} >= 1 and has the solutions x >= 1.

    Thus, if x > 0 then the solutions are x>= 1.


2.  If x < 0, then the inequality {{{1/x}}} <= x is equivalent to {{{x^2}}} <= 1 and has the solutions -1 <= x < 0.

    Thus, if x < 0 then the solutions are -1 <= x < 0.
</pre>

<U>Answer</U>.  &nbsp;&nbsp;The solution set is &nbsp;&nbsp;[-1,0)&nbsp; U &nbsp;[1,{{{infinity}}}).


<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -5.5,5.5, -5.5, 5.5,
          1/x, x
)}}}


Plots &nbsp;&nbsp;f(x) = &nbsp;{{{1/x}}} &nbsp;(red) &nbsp;and &nbsp;g(x) = x &nbsp;(green)

  </TD>
  </TR>
</TABLE>