First slide

Continuity

Question

$If f (x) is a continuous function \forall x \in R and f (x) \in (1, \sqrt{30}) and g (x) = [\frac{f (x)}{a}] where$ [.] denotes the greatest integer function is continuous then the least positive integral value of a is

Moderate

Solution

$g (x) = [\frac{f (x)}{a}] is continuous if [\frac{f (x)}{a}] = 0 for \forall f (x)$
$f (x) \in (1, \sqrt{30}) for which we must have a > \sqrt{30}$
Hence the least value of a is 6.

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