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Question 1032014: a number minus its reciprocal is less than zero. find the numbers and answer in interval notaion
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x=number
(1/x)=reciprocal
x-(1/x) <0
x^2-1 <0, multiplying through by x.
x^2<1
x<1, x<-1 are the possibilities
x<-1, and if -2 is the number, the reciprocal is (-1/2) and the difference is less than 0. x=-1/2, reciprocal is -2, and -1/2-(-2) is >0.
x<1. If (1/2) were used, 1/2-2 are less than 0. If (1/1000) were used, 1/1000-1000 is less than 0.
x=0; there is no number or reciprocal doesn't exist here.
(-oo,-1)U(0,1)
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
a number minus its reciprocal is less than zero. find the numbers and answer in interval notaion
After forming and solving the INEQUALITY, you should find the CRITICAL POINTS to be: - 1, 0, and 1.
Hence, there are 4 INTERVALS that you need to test. They are:  .
The intervals that satisfy the INEQUALITY will be your answer. Put in INTERVAL NOTATION.
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