Question

True or false? The absolute value is not one to one, but the greatest integer function is

Answer 1

The answer would be false because absolute value isn't one to one

Answer 2

The given statement is false.

Explanation:

One-One function

A one-one function is a function such that for every value in domain there is exactly one point in domain.

Or in other words it can be written as:

`f(x) = f(y) \Rightarrow x = y`

The absolute value function is not one-one.

This can be explained with the help of an example:

`\mid a \mid = a, a > 0\\~~~~~ = -a, a < 0`

`\mid 3 \mid = \mid -3 \mid = 3`

Thus, for two values in co-domain it have same values in range.

The greatest integer function is not one-one. This can be shown with the help of a counter example:

`f(x) = [x]`

`f(1) = f(1.2) = f(1.5) = f(1.9) = 1`

Since for multiple values in domain, we have the same value in range, there greatest integer function is not one-one.