First slide

Functions (XII)

Question

$Let f : (- \infty, 0] \to [1, \infty) be defined as$ $f (x) = (1 + \sqrt{- x}) - (\sqrt{- x} - x), then f (x) is$

Moderate

A

injective but not surjective
B

injective as well as surjective
C

neither injective nor surjective
D

surjective but not injective

Solution

$f (x) = (1 + \sqrt{- x}) - (\sqrt{- x} - x)$
$= 1 - x, x \leq 0$
$Then 1 - x \geq 1$
Hence function is injective and surjective

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