Answer: The function is not one-to-one
Step-by-step explanation:
An one-to-one function is such that no two elements in the domain correspond to the same element in the range.
Now, we have the function:
y = f(x) = round(x)
Which rounds x to the nearest whole number.
Now, to round to the next whole number we must look at the first number after the decimal point.
If that number is 5 or larger, we round up
If that number is smaller than 5, we round down.
Then, for example:
f(1.2) = 1
because the first number after the decimal point is smaller than 5.
and:
f(1.1) = 1
f(1.2) = 1
f(1.2423) = 1
f(1.348) = 1
So we have a lot (if x is real, we have infinite) values of x that are maped into the same value in the range.
Then this can not be an one-to-one function.
