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If f(x) is a continuous function \mathrm{\forall x \in R} and the range of \mathrm{f(x)=(2, \sqrt{26})} and \mathrm{g(x)=\left[\frac{f(x)}{a}\right]} is continuous \mathrm{\forall x \in R}( [.] denotes the greatest integer function), then the least positive integral value of a is

Option: 1

2


Option: 2

3


Option: 3

6


Option: 4

5


Answers (1)

best_answer

Since g(x) is continuous \forall x \in R, g(x) should be constant. Since \mathrm{f(x) \in(2, \sqrt{26}), a \geq \sqrt{26},} (as

\mathrm{\left.\left[\frac{f(x)}{\sqrt{26}}\right]=0 \forall x \in R\right).}

So least integral value of a is 6 .

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Nehul

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