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Q.

The value of the parameter $α,$ for which the function $f (x) = 1 + α x, α \neq 0$ is the inverse of itself, is

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a

$- 2$

b

2

c

$- 1$

d

1

answer is B.

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Detailed Solution

$f (x) = f^{- 1} (x) = f {f (x)} = x$

$\Rightarrow (1 + α) = x (1 - α^{2})$

$∴$ it is satisfied only for $α = - 1$

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The value of the parameter α, for which the function f(x)=1+αx,α≠0 is the inverse of itself, is