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Question

The number of solutions for [[x]x]=sinx is (where [.] denotes the greatest integer function) is

A
5
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B
7
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C
0
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D
infinite
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Solution

The correct option is D infinite
f(x)=[[x]x] =[(x[x])] =[{x}]

{x}=0 xZ
0<{x}<1Z/

f(x)=[{x}]={0,xZ1,xZ/

sinx[1,1]


From graph, it is clear that there are infinite number of solutions.

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