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Byju's Answer
Standard XII
Mathematics
Graph of Fractional Part Function
The number of...
Question
The number of solutions of the equation
[
3
x
]
−
[
x
+
1
]
=
3
x
, where
[
.
]
denotes greatest integer function, is equal to
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Solution
[
3
x
]
−
[
x
+
1
]
=
3
x
⇒
−
[
x
+
1
]
=
3
x
−
[
3
x
]
⇒
−
[
x
+
1
]
=
{
3
x
}
where
{
.
}
denotes fractional integer function
Now,
0
≤
{
3
x
}
<
1
∴
−
[
x
+
1
]
=
0
⇒
[
x
+
1
]
=
0
⇒
0
≤
x
+
1
<
1
−
1
≤
x
<
0
⇒
−
3
≤
3
x
<
0
⇒
[
3
x
]
=
−
3
,
−
2
,
−
1
Now,
[
3
x
]
−
0
=
3
x
⇒
3
x
=
−
3
,
−
2
,
−
1
x
=
−
3
3
,
−
2
3
,
−
1
3
x
=
−
1
,
−
2
3
,
−
1
3
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Standard XII Mathematics
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