SOLUTION: the solution set of the inequality 1/x<=x is ?

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Question 1044462: the solution set of the inequality 1/x<=x is ?
Answer by ikleyn(52797) About Me  (Show Source):
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the solution set of the inequality 1/x<=x is ?
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1.  If x > 0, then the inequality 1%2Fx <= x is equivalent to x%5E2 >= 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%2Fx <= x is equivalent to x%5E2 <= 1 and has the solutions -1 <= x < 0.

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

Answer.   The solution set is   [-1,0)  U  [1,infinity).


graph%28+330%2C+330%2C+-5.5%2C5.5%2C+-5.5%2C+5.5%2C%0D%0A++++++++++1%2Fx%2C+x%0D%0A%29

Plots   f(x) =  1%2Fx  (red)  and  g(x) = x  (green)