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  4. The number of discontinuities of the greatest integer function f(x)=[x],x∈ ( -(7/2),100 ) is equal to

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Q. The number of discontinuities of the greatest integer function $ f(x)=[x],x\in \left( -\frac{7}{2},100 \right) $ is equal to

KEAMKEAM 2009Continuity and Differentiability

Solution:

Given, $ f(x)=[x],x\in (-3.5,100) $
As we know greatest integer is discontinuous on integer values. In given interval, the integer values are $ (-3,-2,-1,0,\text{ }...,99)
$
$ \therefore $ Total number of integers are 103.