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Byju's Answer
Standard XII
Mathematics
Definition of Function
If f:R→ R i...
Question
If
f
:
R
→
R
is defined by
f
(
x
)
=
2
x
−
3
∀
x
ϵ
R
, which of the following is / are correct?
A
f
is a function
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B
f
is an injection
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C
f
is surjection
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D
f
is not onto
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Solution
The correct option is
A
f
is a function
Graph of
f
(
x
)
=
2
x
−
3
is a straight line as shown in the figure.
If we draw a line parallel to
y
axis it will cut the graph at only one point.
So, it represents a function.
Option A is correct.
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Similar questions
Q.
Let
f
:
R
→
R
be a function defined by
f
x
=
e
|
x
|
-
e
-
x
e
x
+
e
-
x
.
Then
,
(a) f is a bijection
(b) f is an injection only
(c) f is surjection on only
(d) f is neither an injection nor a surjection
Q.
If
f
:
R
→
R
be defined by
f
(
x
)
=
e
x
and
g
:
R
→
R
be defined by
g
(
x
)
=
x
2
.
The mapping
g
∘
f
:
R
→
R
be defined by
(
g
∘
f
)
(
x
)
=
g
[
f
(
x
)
]
∀
x
∈
R
,
Then
Q.
Match the following lists :
1)
f
:
R
→
R
defind by
f
(
x
)
=
a
x
+
b
is
(
a
≠
0
)
a) injection but not surjection
2)
f
:
R
→
R
defind by
f
(
x
)
=
[
x
]
is
b) surjection but not injection
3)
f
:
R
→
[
0
,
∞
)
defind by
f
(
x
)
=
|
x
|
is
c) bijection
4)
f
:
N
→
N
defind by
f
(
x
)
=
x
3
is
d) neither injection nor surjection
Q.
The function
f
:
-
1
/
2
,
1
/
2
,
1
/
2
→
-
π
/
2
,
π
/
2
, defined by
f
x
=
sin
-
1
3
x
-
4
x
3
, is
(a) bijection
(b) injection but not a surjection
(c) surjection but not an injection
(d) neither an injection nor a surjection
Q.
Let
f
:
R
→
R
be a function defined by
f
(
x
)
=
x
3
+
x
2
+
3
x
+
sin
x
.
Then
f
is
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