If N - N is defined by f n - n -1 n- thenA- f is one-one but not ontoB- f is both one-one and ontoC- f is neither one-one nor ontoD- f is onto but not one-one

The correct option is B f is both one one and ontoThis function f maps 1→ 2, 2→ 1 3→ 4, 4→ 3 5→ 6, 6→ 5 i.e., 2m 1→ 2m and 2m→ 2m 1 So f is one one and onto. ...

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Standard XII

Mathematics

Bijective Function

If N → N is d...

Question

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

f is one-one but not onto

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f is both one-one and onto

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f is neither one-one nor onto

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f is onto but not one-one

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Solution

The correct option is B f is both one-one and onto
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.

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

The correct option is B f is both one-one and ontoThis function f maps 1→2,2→1 3→4,4→3 5→6,6→5 i.e., 2m−1→2m and 2m→2m−1 So f is one-one and onto.

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

The correct option is B f is both one-one and onto
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.