If f-N- N is defined by fx-2x-5 then f is

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Standard XII

Mathematics

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If f:N→ N is...

Question

If $f : N \to N$ is defined by $f (x) = 2 x + 5$ then $f$ is

one-one only

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onto only

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bijective

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neither one - one nor onto

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Solution

The correct option is A one-one only
$f (x) = 2 x + 5$
$f^{'} (x) = 2$ i.e. increasing function (one - one)
But it is not onto because $f (x)$ does not take all values in $N$
Range of $f (x) \neq$ codomain

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Iff:N→N is defined by f(x)=2x+5 then f is

The correct option is A one-one onlyf(x)=2x+5f′(x)=2 i.e. increasing function (one - one)But it is not onto because f(x) does not take all values in NRange of f(x)≠ codomain

If $f : N \to N$ is defined by $f (x) = 2 x + 5$ then $f$ is

The correct option is A one-one only
$f (x) = 2 x + 5$
$f^{'} (x) = 2$ i.e. increasing function (one - one)
But it is not onto because $f (x)$ does not take all values in $N$
Range of $f (x) \neq$ codomain