First slide

Functions (XII)

Question

$Let f : (2, 4) \to (1, 3) where f (x) = x - [\frac{x}{2}] (where [\cdot] denotes the greatest integer function), then f^{- 1} (x) is$

Moderate

A

Not define
B

x - 1
C

x+1
D

None of these

Solution

$f (2, 4) \to (1, 3) . For 2 < x < 4 \Rightarrow 1 < x / 2 < 2$
$\Rightarrow [\frac{x}{2}] = 1 \Rightarrow f (x) = x - [x / 2] = x - 1 \Rightarrow f^{- 1} (x) = x + 1$

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