First slide

Functions (XII)

Question

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

Easy

A

-2
B

-1
C

1
D

2

Solution

$l e t f (x) = 1 + x α = y \Rightarrow x = \frac{y - 1}{α} \Rightarrow f^{- 1} (x) = \frac{x - 1}{α} \sin c e f^{- 1} (x) = f (x) \Rightarrow \frac{x - 1}{α} = 1 + α x$
$\Rightarrow α = - 1$

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