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  • In [1,3] the function  <img alt="\mathrm{\left[x^2+1\right],[x]}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft%5Bx%5E2&plus;1%5Cright%5D%2C%5Bx%5D%7D"

In [1,3] the function  \mathrm{\left[x^2+1\right],[x]}  denoting the greatest integer function, is continuous

Option: 1

for all x


Option: 2

for all x exceptat four points


Option: 3

for all except at seven points


Option: 4

for all except at eight-points


Answers (1)

best_answer

Clearly,  \mathrm{\left[x^2+1\right]}  is discontinuous at \mathrm{x=1, \sqrt{2}, \sqrt{3}, \sqrt{4}, \sqrt{5}, \sqrt{6}, \sqrt{7}, \sqrt{8}}. Note that it is right continuous at x=1 but not left continuous at x=3.

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Pankaj

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