First slide

Functions (XII)

Question

$f : N \to N, where f (x) = x - (- 1)^{x} . Then f is$

Easy

A

one-one and into
B

many-one and into
C

one-one and onto
D

many-one and onto

Solution

$f (x) = x - {(- 1)}^{x}$
$f (x) = x - 1, i f x i s e v e n$
$= x + 1, i f x i s o d d$
so it is one one and onto because $f (1) = 2, f (2) = 1, f (3) = 4, f (4) = 3 . . . . . . . e t c .$

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