True or false? The absolute value is not one to one, but the greatest integer function is
Answer:
The given statement is false.
Step-by-step 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.