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Byju's Answer
Standard XI
Mathematics
Definition of Functions
The value of ...
Question
The value of the parameter
α
,for which the function
f
(
x
)
=
1
+
α
x
,
α
≠
0
is the inverse of itself, is
A
-2
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B
-1
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C
1
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D
2
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Solution
The correct option is
B
-1
y
=
1
+
α
x
⇒
x
=
y
−
1
α
f
−
1
(
x
)
=
x
−
1
α
=
f
(
x
)
=
1
+
α
x
⇒
x
−
1
α
=
1
+
α
x
⇒
x
−
1
=
α
+
α
2
x
Equating the coefficient of x
α
2
=
1
&
α
=
−
1
α
=
−
1
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