If f : N → N is defined by f ( n ) = n − ( − 1 ) n , then

This function f maps: 1 → 2 , 2 → 1 3 → 4 , 4 → 3 5 → 6 , 6 → 5 i.e., 2 m − 1 → 2 m and 2 m → 2 m − 1 . So f is one-one and onto.

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MathematicsFunctionsGeneral (Definition,type and special type)Medium2 min

MathematicsMediumsingle choice

If $f : N \to N$ is defined by $f (n) = n - (- 1)^{n}$ , then

Answer:

Solution:

This function $f$ maps:

$1 \to 2, 2 \to 1 3 \to 4, 4 \to 3 5 \to 6, 6 \to 5$

i.e., $2 m - 1 \to 2 m$ and $2 m \to 2 m - 1$ . So $f$ is one-one and onto.

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:General (Definition,type and special type)

⏱ 2m

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