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Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
Show that the...
Question
Show that the function
f
:
R
→
, defined as
f
(
x
)
=
x
2
, is neither one nor onto.
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Solution
f
(
x
)
=
x
2
b
e
c
a
u
s
e
d
o
m
a
i
n
o
f
x
2
i
s
(
R
)
a
n
d
r
a
n
g
e
i
s
[
0
,
∞
]
⇒
a
n
d
p
u
t
x
=
1
,
a
n
d
−
1
g
i
v
e
s
s
a
m
e
v
a
l
u
e
s
h
e
n
c
e
,
i
t
i
s
(
m
a
n
y
o
n
e
)
.
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0
Similar questions
Q.
Show that the function
f
:
R
→
R
, defined by
f
(
x
)
=
x
2
−
x
2
1
+
x
2
,
is neither one-one nor onto.
Q.
Show that the function
f
:
R
→
R
defined by
f
(
x
)
=
x
x
2
+
1
∀
x
∈
R
is neither one-one nor onto.
Q.
Show that the function
f
:
R
→
R
defined by
f
(
x
)
=
x
x
2
+
1
for all
x
∈
R
is neither one-one nor onto.
Q.
f
:
R
→
R
,
f
(
x
)
=
x
x
2
+
1
Show that function is neither one-one, nor onto.
Q.
Show that the function
f
:
R
→
R
defined by
f
(
x
)
=
x
x
2
+
1
,
∀
x
∈
R
is neither one-one nor onto. Also, if
g
:
R
→
R
is defined as
g
(
x
)
=
2
x
−
1
, find
f
o
g
(
x
)
.
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Definition of a Determinant
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