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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Prove that th...
Question
Prove that the function
f
:
R
→
R
given by
f
(
x
)
=
3
x
+
3
is one-one and onto.
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Solution
To prove that the function is one-one, we have to prove that if
f
(
x
1
)
=
f
(
x
2
)
, then
x
1
=
x
2
Let
f
(
x
1
)
=
f
(
x
2
)
⇒
3
x
1
+
3
=
3
x
2
+
3
⇒
x
1
=
x
2
∴
f
(
x
)
is one-one.
For onto,
Let
f
(
x
)
=
y
,
where
y
∈
R
⇒
y
=
3
x
+
3
⇒
x
=
y
−
3
3
For all
y
∈
R
⇒
x
∈
R
∴
f
(
x
)
is onto.
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Q.
Prove that function
f
:
R
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R
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)
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prove that function "f" defined as
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:
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)
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)
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