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AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 160
If
f
:
R
→
R
is defined by
f
(
x
)
=
[
2
x
]
−
2
[
x
]
for
x
∊
R
,
then the range of
f
is (Here
[
x
]
denotes the greatest integer not exceeding
x
)
Z
,
the set of all integers
N
,
the set of all natural numbers
R
,
the set of all real numbers
{0, 1}
Validate
Solution:
The function is given as.
f
(
x
)
=
[
2
x
]
−
2
[
x
]
for
x
∈
R
The
x
is comes out as.
x
=
[
x
]
+
{
x
}
2
x
=
2
[
x
]
+
2
{
x
}
[
2
x
]
=
2
[
x
]
+
(
2
[
x
]
)
The range for function
2
x
is,
[
2
x
]
=
{
2
[
x
]
+
0
,
0
<
{
x
}
<
1
2
2
[
x
]
+
1
,
1
2
≤
{
x
}
<
1
Putting the values in given function.
[
2
x
]
−
2
[
x
]
=
{
0
,
0
≤
{
x
}
<
1
2
1
,
1
2
≤
{
x
}
<
1
Thus, the range of the function is
{
0
,
1
}
.
© examsnet.com
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