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  • If f(x) is a continuous function  <img alt="\forall\,\, x \in R" src="/latex-image/?%5Cforall%5C%2C%5C%2C%20x%20%5Cin%

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