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If f(x) is a continuous function ∀x∈R and f(x)∈(1,30) and g(x)=f(x)a where [.] denotes the greatest integer function is continuous  then the least positive integral value of a is

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answer is 0006.00.

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Detailed Solution

g(x)=f(x)a is continuous if f(x)a=0 for ∀f(x)f(x)∈(1,30) for which we must have a>30Hence the least value of a is 6.
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If f(x) is a continuous function ∀x∈R and f(x)∈(1,30) and g(x)=f(x)a where [.] denotes the greatest integer function is continuous  then the least positive integral value of a is