3
You visited us
3
times! Enjoying our articles?
Unlock Full Access!
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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
onto
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
one-one onto
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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.
Suggest Corrections
0
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
]
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Types of Functions
MATHEMATICS
Watch in App
Explore more
One - One function
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app