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inequalities

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inequalities

by sud21 » Sun Jan 15, 2012 2:27 am
-1<x<-3/4, which of the following has the greatest value?
-x, -1/x, 1-1/x, 1/(1+x)
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by kanwar86 » Sun Jan 15, 2012 2:33 am
sud21 wrote:-1<x<-3/4, which of the following has the greatest value?
-x, -1/x, 1-1/x, 1/(1+x)
As -1<x<-3/4
Choose any value of x satisfying the above inequality.
For simplicity, choose x=-4/5
-x= 4/5
-1/x = 5/4
1-1/x = 1+5/4=9/4
1/(1+x) = 1/(1/5) = 5
So, greatest value is 1/(1+x) = 5
Regards

Kanwar

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by ronnie1985 » Sun Jan 15, 2012 8:41 pm
For 0<x,1, 1/x is a increases with with decreasing x. Since -1<x<-3/4, -1/x>1, but (1+x)<|x| = 1/(1+x)>-1/x
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