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Test Index
AP EAPCET 08-Jul-2022 Shift 2 Paper
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 160
If the function
f
:
R
→
R
is defined by
f
(
x
)
=
x
|
x
|
, then
f
is one-one but not onto
f
is onto but not one-one
f
is both one-one and onto
f
is neither one-one nor onto
Validate
Solution:
Given,
f
(
x
)
=
x
|
x
|
=
[
x
(
x
)
,
x
≥
0
x
(
−
x
)
,
x
<
0
]
⇒
f
(
x
)
=
[
x
2
,
x
≥
0
−
x
2
,
x
<
0
]
Also,
f
:
R
→
R
According to the graph-
domain
of
f
(
x
)
=
Range
of
f
(
x
)
=
R
∴
Range
=
Codomain
=
R
⇒
f
(
x
)
is an onto function.
If a line parallel to
X
−
axis
is drawn, it will intersects at only one point of
f
(
x
)
Hence,
f
(
x
)
is one-one also.
© examsnet.com
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