Question
Download Solution PDFThe function f(x) = [x] where [x] the greatest integer function is continuous at
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
To find the point of discontinuity of the function f(x) = [x], draw the graph of the function f(x) = [x].
Greatest Integer Function: (Floor function)
The function f (x) = [x] is called the greatest integer function and means greatest integer less than or equal to x i.e [x] ≤ x.
The domain of [x] is R and range is I, where R is the set of real numbers and I is the set of integers.
From the graph, we can say that the function is discontinuous at every integer.
The function f ( x )= [x] is continous for all x , except integral valaues of x .
∴ It is continuous at x = 1.5, which is not an integer.
The correct option is 4.
Last updated on Dec 17, 2024
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