The function $f : N \to N$ defined by $f (x) = x - 5 [\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less then or equal to $x$ is

One-one and onto

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One-one but not onto

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Onto but not one-one

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Neigher one-one nor onto

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Solution

The correct option is B One-one but not onto
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Similar questions

Q. Prove that the function f : N → N, defined by f(x) = x² + x + 1, is one-one but not onto.

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(a) neither one-one nor onto
(b) one-one but not onto
(c) onto but not one-one
(d) one-one and onto both

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The function f:N→N defined by f(x)=x−5[x5], where N is the set of natural numbers and [x] denotes the greatest integer less then or equal to x is

The correct option is B One-one but not ontoundefined

The function $f : N \to N$ defined by $f (x) = x - 5 [\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less then or equal to $x$ is

The correct option is B One-one but not onto
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