The greatest integer function f : R R, given by f(x) = [x] is:

Question

The greatest integer function $f : R \to R$ , given by $f (x) = [x]$ is:

Smart Achievers · Accepted Answer

(4)

Ans. neither one-one nor onto

Explanation:

We know

[2.2] = 2

[2.5] = 2

$∵$ [2.2] = [2.5]

but 2.2 ≠ 2.5

$\Rightarrow f$ is not one-one function.

Now, consider $0.6 \in R$

It is known that $f (x) = [x]$ is always an integer. Thus, there does not exist any element $x \in R$ such that $f (x) = 0.6$ .

$∴$ $f$ is not onto.

Hence, greatest integer function is neither one-one nor onto.

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