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

Question

asked Jan 2, 2017 185k views

2 Answers

Rfanatic · Answer 1 · 2017-01-08T22:40:32+0000

Answer:

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.