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

Let $y = f (x)$ $\Rightarrow y = 1 + α x \Rightarrow x = \frac{y - 1}{α}$
$\Rightarrow f^{- 1} (y)$ $= \frac{y - 1}{α}$

Now, $f (x) = f^{- 1} (x)$ $\Rightarrow 1 + α x = \frac{x - 1}{α}$

$\Rightarrow 1 + α x = \frac{1}{α} x - \frac{1}{α}$

$\Rightarrow α = \frac{1}{α} and 1 = - \frac{1}{α} \Rightarrow α = - 1$

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