NIMCET 2009 Question Paper with solutions

Question : 21 of 120

Marks: +1, -0

Let

f(x)=[x^{2}-3]

where [ ] denotes the greatest integer function. Then the number of points in the interval

(1,2)

where the function is discontinuous is

Solution:

f(c)=[x^{3}-3] in(1,2)

gives

f(x)=\{\table -2 {;}1 < x < √{2} ; -1{ ; }√{2} ≤ x < √{3} ; 0 {;} √{3} ≤ x < 2.

From above, we see that

f(x)

is discontinuous at two points. Viz.

√{2}

and

√{3}

in the interval

(1,2)

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