Define greatest integer function ? What is domain and range of it ?

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Karthik Ganeshan

MCA ,BSC(COMPUTER SCIENCE)

The greatest integer function of a real number x is represented by f(x) = or |_x_|. For all real numbers x, the greatest integer function returns the largest integer less than or equal to x Domain and Range: f(x) = is defined for all x, so the domain is (-infinity, infinity). Now, since f(x)...
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The greatest integer function of a real number x is represented by f(x) = [x] or |_x_|. For all real numbers x, the greatest integer function returns the largest integer less than or equal to x Domain and Range: f(x) = [x] is defined for all x, so the domain is (-infinity, infinity). Now, since f(x) = [x] gives the largest integer equal to or less than x, [x] outputs only integers by definition. Thus, the range of f(x) = [x] is all integers. read less
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Tutor

The greatest integer function also known as floor function is defined as follows:- f(x)= ?x? returns the largest integer less than or equal to x. in set notation it is defined as =max {m epsilon Z | m<=x}. Z is set of all integers. The domain for f(x) is R. x can take any real value. And the...
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The greatest integer function also known as floor function is defined as follows:- f(x)= ?x? returns the largest integer less than or equal to x. in set notation it is defined as [x]=max {m epsilon Z | m<=x}. Z is set of all integers. The domain for f(x) is R. x can take any real value. And the range is Z. read less
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Tutor

Format is not getting accepted on this website ....for the floor function symbol...it looks something like Lx_|....essentially square brackets with upper edges removed.
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Tutor

Very easy...An integer, less than or equal to that number. eg. = 4 , = 4, = 4
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btech

DOMAIN SET OF REAL NUMBERS, RANGE [0,1)
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Maths and Physics Tutions

Note that f(x) = is defined for all x, so the domain is (-infinity, infinity). Now, since f(x) = gives the largest integer equal to or less than x, outputs only integers by definition. Thus, the range of f(x) = is all integers.
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An Engineer from IIEST, Shibpur wants to teach Maths.

The greatest integer function (Ceiling Function) returns the largest integer less than or equal to x, for all real numbers x. The greatest integer function rounds down a real number to the nearest integer. e.g. = 2; = 1; = -4; = -7.
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B.tech in [E&T]

Previous integer simple definition
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Trainer

In which subject u r asking?
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Mathematics for JEE Mains/Advanced, XI & XII (All Boards)

= Greatest Integer less than or equal to x. Graphically, plot the point on the number line and take the nearest integer just left of it. If the number is itself an integer than = x. Domain: R. All real numbers Range: Z. All integers
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