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Byju's Answer
Standard XII
Mathematics
One - One function
If f : [0, ...
Question
If
f
:
[
0
,
Π
]
→
[
−
1
,
1
]
, f(x) = cosx, then f is.
A
one-one
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B
onto
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C
one-one onto
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D
none of these
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Solution
The correct option is
D
one-one onto
f takes all values from
[
−
1
,
1
]
while travelling from
[
0
,
π
]
. None of the values are repeated either.
Hence it is one-one and onto.
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Similar questions
Q.
If
f
:
[
0
,
π
]
→
R
,
f
(
x
)
=
cos
x
, then
f
is
Q.
Let
f
:
(
−
1
,
1
)
→
B
, be a function defined by
f
(
x
)
=
t
a
n
−
1
2
x
1
−
x
2
, then f is both one - one and onto when B is the interval
Q.
f(x) = sin(x) defined on f:
[
−
π
2
,
π
2
]
→
[
−
1
,
1
]
is -
Q.
If,
f
(
x
)
=
⎡
⎢
⎣
x
tan
−
1
x
+
sec
−
1
1
x
,
x
ϵ
(
−
1
,
1
)
−
0
π
2
i
f
x
=
0
⎤
⎥
⎦
then
f
′
(
0
)
is
Q.
Assertion :
f
is a function defined on the interval
[
−
1
,
1
]
such that
f
(
sin
2
x
)
=
sin
x
+
cos
x
Statement I: If
x
∈
[
−
π
4
,
π
4
]
, then
f
(
tan
2
x
)
=
sec
x
Reason: Statement II:
f
(
x
)
=
√
1
+
x
,
∀
x
∈
[
−
1
,
1
]
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