Domain Is Greatest Integer Function
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It is also known as floor of x.
Domain is greatest integer function. The greatest functions are defined piecewise its domain is a group of real numbers that are divided into intervals like 4 3 3 2 2 1 1 0 and so on. Then means if x lies in n n 1 then the greatest integer function of x will be n. You can put any number in for x and it will round it down to the nearest integer.
Greatest integer function is a piece wise function also called step function because of its graph. The output is based on the input and there are two rules that need to be followed while writing the output. The function is defined everywhere.
This is also called the floor function. There are no x intercepts. If we examine a number line with the integers and 1 3 plotted on it we see.
For example the greatest integer function of the interval 3 4 will be 3. The largest integer that is less than 2 7 is 2. Math lfloor x rfloor n x in n n 1 math where math n in mathbb z math.
X the largest integer that is less than or equal to x. If. The output is going to be an integer if the input is an integer.
So lfloor 2 7 rfloor 2. This post contain in depth explain of greatest integer function its graph domain and range along with a lot of solved examples. The greater integer function is a function that gives the output of the greatest integer that will be less than the input or lesser than the input.
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