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Byju's Answer
Standard XII
Mathematics
Definition of Sets
Let f be fu...
Question
Let
f
be function from
R
t
o
R
given by
f
(
x
)
=
x
2
−
4
x
2
+
1
.
Then
f
(
x
)
is
A
one-one and into
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B
one-one and onto
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C
many-one and into
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D
many-one and onto
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Solution
The correct option is
C
many-one and into
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0
Similar questions
Q.
Let
f
:
(
−
1
,
1
)
→
B
be a function defined by
f
(
x
)
=
tan
−
1
2
x
1
−
x
2
, then
f
is both one-one and onto when B is the interval
Q.
If
f
:
(
−
1
,
1
)
→
B
, is a function defined by
f
(
x
)
=
tan
−
1
2
x
1
−
x
2
, then find
B
when
f
(
x
)
is both one-one and onto function.
Q.
Let a function
f
:
R
→
R
be defined as
f
(
x
)
=
x
2
−
x
2
1
+
x
2
for all
x
∈
R
. Then state whether
f
is one-one or onto ?
Q.
Let
f
:
R
→
R
be a function defined by
f
x
=
x
2
-
8
x
2
+
2
. Then, f is
(a) one-one but not onto
(b) one-one and onto
(c) onto but not one-one
(d) neither one-one nor onto
Q.
Let
f
:
[
0
,
√
3
]
→
[
0
,
π
3
+
l
o
g
e
2
]
defined by
f
(
x
)
=
l
o
g
e
√
x
2
+
1
+
t
a
n
−
1
x
then f(x)is
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