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Byju's Answer
Standard XII
Mathematics
Derivative of One Function w.r.t Another
25. Prove tha...
Question
25. Prove that the function f:N to N defined by f(x) =3x-2 is one-one but not onto.
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Similar questions
Q.
Prove that the function f : N → N, defined by f(x) = x
2
+ x + 1, is one-one but not 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 the function
f
:
R
-
-
b
→
R
-
1
be defined by
f
x
=
x
+
a
x
+
b
,
a
≠
b
.
T
hen
,
(a) f is one-one but not onto
(b) f is onto but not one-one
(c) f is both one-one and onto
(d) None of these
Q.
Prove that the function
f
:
N
→
N
,
defined by
f
(
x
)
=
x
2
+
x
+
1
is one-one but not onto. Find inverse of
f
:
N
→
S
, where
S
is range of
f
.
Q.
If a function
f
is defined as
f
:
Z
→
Z
,
f
(
n
)
=
{
n
2
:
n
is even
−
n
+
1
2
:
n
is odd
then prove that
f
is onto but not one-one.
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