First slide

Functions (XII)

Question

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

Moderate

A

$- 2$
B

$- 1$
C

1
D

2

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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