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Find the value of parameter alpha for...

Find the value of parameter `alpha` for which the function `f(x)=1+alpha\ x` , `alpha!=0` is the inverse of itself.

A

`-2`

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
It is given that `f:R to R` is given by `f(x)=1+alpha x, alpha ne 0` is inverse of itself.
`therefore fof f(x)=x"for all "x in R`
`Rightarrow f(f(x))=x"for all "x in R`
`Rightarrow f(1+alpha x)=x"for all "x in R`
`Rightarrow 1+alpha(1+alpha x)=x"for all "x in R`
`Rightarrow x(alpha^(2)-1)+(alpha+1)=0"for all "x in R`
`Rightarrow alpha^(2)-1=0 and alpha+1=0 Rightarrow alpha=-1`
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