If gx is a continuous function - x- and the range of fx is 2-26 and gx-fxc- is continuous - x- then the positive value of c is where - denotes the greatest integer function

The correct option is D 6 Given g(x) is a continuous function ∀ x∈ℝ and the range of f(x) is (2,√(26)) and g(x)=[f(x)c] is c ...

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Standard XII

Mathematics

Absolute Value Function

If gx is a ...

Question

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

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Solution

The correct option is D $6$
Given $g (x)$ is a continuous function $\forall x \in R$ and the range of $f (x)$ is $(2, \sqrt{26})$ and $g (x) = [\frac{f (x)}{c}]$ is continuous $\forall x \in R$

Hence for $g (x)$ to be continuous, $c > \sqrt{26}$ .

Because if we take any value of $c$ between $(2, \sqrt{26})$ like $3, 4, 5$ then, when $f (x)$ varies from $2 t o \sqrt{26}$ and due to greatest integer function $g (x)$ become discontinuous at $c = 3, 4, 5$ .
So, for continuity $c = 6$ .

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If g(x) is a continuous function ∀x∈R and the range of f(x) is (2,√26) and g(x)=[f(x)c] is continuous ∀x∈R, then the positive value of c is (where [.] denotes the greatest integer function)

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