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Question

The value of the parameter α ,for which the function f(x)=1+αx,α0 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+αxx=y1α
f1(x)=x1α=f(x)=1+αxx1α=1+αxx1=α+α2x
Equating the coefficient of x
α2=1 & α=1
α=1

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