Question

Consider the function ( ) round( ) f xx , which rounds the input, x, to the nearest integer. Is this function one-to-one? Explain or justify your answer.

Answer 1

It is not a one to one function

Explanation:

Required

Determine if f(x) = round(x) is a one to one function

This question is best answered using illustrating values;

Let x = 1.1

f(x) = round(x) becomes

f(1.1) = round(1.1)

f(1.1) = 1

Let x = 1.3

f(x) = round(x) becomes

f(1.3) = round(1.3)

f(1.3) = 1

Notice that for the two values of x, f(x) has the same value of 1.

This two illustrating values can be used to conclude that the fuction is not one-to-one.