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greatest integer function

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greatest integer function

by sanju09 » Wed Apr 01, 2009 2:47 am
The greatest integer function for a given number is equal to the integer it has last exceeded, for a number x, its greatest integer function is denoted by [x].

If │x + 2│ = x + 2; and [x] = 3, and x is an integral multiple of 0.9. Find x.
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Re: greatest integer function

by marcusking » Wed Apr 01, 2009 5:33 am
sanju09 wrote:The greatest integer function for a given number is equal to the integer it has last exceeded, for a number x, its greatest integer function is denoted by [x].

If │x + 2│ = x + 2; and [x] = 3, and x is an integral multiple of 0.9. Find x.
We know from │x + 2│ = x + 2 that x must be positive
From the definition of [x] if [x]=3 then x must be 4

4 * 0.9 = 3.6

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by sanju09 » Wed Apr 01, 2009 6:05 am
From the definition of [x] if [x]=3 then x must be 4

4 * 0.9 = 3.6


Let me elaborate the meaning of [x] here; the value of [x] is the greatest integer that has been surpassed by x while moving from left to right on the real number line. For example [5.22] = 5 and [5] = 5 or [-7.34] = -8 and [-7] = -7 and like that. Here, if [x] = 3, it means that 3 &#8804; x < 4; see 4 is not inclusive here, and 3 cannot be entertained simply because of the fact that 3 is not an integral multiple of 0.9. The only integral multiple of 0.9 in the range 3 &#8804; x < 4 is 3.6, hence x = 3.6.

Answerwise you were correct, but...
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