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Question

Find the number of points of discontinuity for f(x)=[6 sinx], 0xπ (Where [.] denotes the greatest integer function)

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Solution

f(x)=[6sinx],0xπ ([.] is G.I.F.)
Range of sinx is [0,1], when xϵ[0,π]
Then range of 6sinx is [0,6]
As f(x) is a G.I.F, it is discontinuous at all integers in its domain, domain of f(x)is range of 6sinx
No. of points of discontinuity=no. of integers in [0,6]
=7

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