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If f(x) is continuous function \forall \mathrm{x} \in \mathrm{R} and the range of \mathrm{f}(\mathrm{x}) \text { is }(2, \sqrt{26}) \text { and } \mathrm{g}(\mathrm{x})=\left[\frac{\mathrm{f}(\mathrm{x})}{\mathrm{c}}\right]

is continuous \forall \mathrm{x} \in \mathrm{R}  then the least positive integral value of c is (where [.] denotes the greatest integer function) 

 

Option: 1

2


Option: 2

3


Option: 3

5


Option: 4

6


Answers (1)

best_answer

\begin{aligned} & 2<\mathrm{f}(\mathrm{x})<\sqrt{26} \\ & \therefore \frac{2}{\mathrm{c}}<\frac{\mathrm{f}(\mathrm{x})}{\mathrm{c}}<\frac{\sqrt{26}}{\mathrm{c}} \\ & \end{aligned}

since, g(x)=\left[\frac{f(x)}{c}\right]  is continuous \forall \mathrm{x} \in \mathrm{R} \Rightarrow \mathrm{g}(\mathrm{x})=0 \text { for } \mathrm{c}=6

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