On the set of all integers defined as f-Z- Z such that fx - -x- then it is-

The correct option is D an identity functionFor all integers [x]=x ∴ f:Z→ Z ; f(x)=[x]=x ∴ f is an identity function. ...

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Standard XII

Mathematics

Definition of Function

On the set of...

Question

On the set of all integers defined as $f : Z \to Z$ such that $f (x) = [x]$ , then it is:

not a function

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a many-to-one function

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an into function

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an identity function

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Solution

The correct option is D an identity function
For all integers $[x] = x$
$∴ f : Z \to Z; f (x) = [x] = x$
$∴ f$ is an identity function.

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Similar questions

Q. Show that the function

f : Z \to Z

defined by

f (x) = x^{2} + x \forall x \in Z

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Q. Let N denote the set of all non-negative integers and Z denote the set of all integers. The function

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Let f(x) be a real valued function defined on: $R \to R$ such that $f (x) = [x]^{2} + [x + 1] - 3$ , where [x] denotes greatest integer less than or equal to x, then which of the following option(s) is/are correct?

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On the set of all integers defined as f:Z→Z such that f(x)=[x], then it is:

The correct option is D an identity functionFor all integers [x]=x∴f:Z→Z;f(x)=[x]=x∴f is an identity function.

On the set of all integers defined as $f : Z \to Z$ such that $f (x) = [x]$ , then it is:

The correct option is D an identity function
For all integers $[x] = x$
$∴ f : Z \to Z; f (x) = [x] = x$
$∴ f$ is an identity function.