At which points the function f x - x - x- where - is greatest integer function- is discontinuousA- Only positive integersB- All positive and negative integers and 0-1C- All rational numbersD- None of these

The correct option is B All positive and negative integers and (0, 1)(i) When 0 ≤ x lt; 1 f(x) doesn't exist as [x] = 0 here. (ii) Also lim_x → 1+f(x) and l ...

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Standard XII

Mathematics

Statement

At which poin...

Question

At which points the function $f (x) = \frac{x}{[x]}$ , where [.] is greatest integer function, is discontinuous

Only positive integers

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All positive and negative integers and (0, 1)

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All rational numbers

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None of these

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Solution

The correct option is B All positive and negative integers and (0, 1)
(i) When 0 $\leq$ x < 1
f(x) doesn't exist as [x] = 0 here.
(ii) Also ${lim}_{x \to 1 +} f (x)$ and ${lim}_{x \to 1 -} f (x)$ does not exist.
Hence f(x) is discontinuous at all integers and also in (0, 1).

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At which points the function f(x)=x[x], where [.] is greatest integer function, is discontinuous

The correct option is B All positive and negative integers and (0, 1)(i) When 0 ≤ x < 1 f(x) doesn't exist as [x] = 0 here. (ii) Also limx→1+f(x) and limx→1−f(x) does not exist. Hence f(x) is discontinuous at all integers and also in (0, 1).

At which points the function $f (x) = \frac{x}{[x]}$ , where [.] is greatest integer function, is discontinuous

The correct option is B All positive and negative integers and (0, 1)
(i) When 0 $\leq$ x < 1
f(x) doesn't exist as [x] = 0 here.
(ii) Also ${lim}_{x \to 1 +} f (x)$ and ${lim}_{x \to 1 -} f (x)$ does not exist.
Hence f(x) is discontinuous at all integers and also in (0, 1).