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The function f(x) = [x]2 – [x2] (where [y] is the greatest integer less than or equal to y), is discontinuous at 
  • a)
    all integers
  • b)
    all integers except 0 and 1
  • c)
    all integers except 0
  • d)
    all integers except 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The function f(x) = [x]2 – [x2] (where [y] is the greatest integ...
We have f (x) = [x]2 – [x2]
At x = 0,

f (1) = [1]2 – [12] = 1 – 1 = 0
∴ L.H.L. = R.H.L. = f (1)
∴ f (x) is continuous at x = 1.
Clearly at other integral pts f (x) is not continuous.
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Most Upvoted Answer
The function f(x) = [x]2 – [x2] (where [y] is the greatest integ...
The function f(x) = [x]^2 represents the square of the greatest integer less than or equal to x. In other words, it rounds down x to the nearest integer and then squares it. For example, if x = 2.5, [x] = 2, and f(x) = 2^2 = 4. If x = -3.8, [x] = -4, and f(x) = (-4)^2 = 16.
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The function f(x) = [x]2 – [x2] (where [y] is the greatest integer less than or equal to y), is discontinuous ata)all integersb)all integers except 0 and 1c)all integers except 0d)all integers except 1Correct answer is option 'D'. Can you explain this answer?
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