The function f x defined as f x - x -42A- continuous but not differentiable - x - RB- continuous and differentiable - x - RC- not continuous at x -4D- continuous only for X - 4

The correct option is A continuous but not differentiable ∀ x ϵ R f(x)= √((x 4)^2) = |x 4| |x 4| is continuous ∀ x ϵ R It is not differntiable at x = 4 ...

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Standard XI

Mathematics

Continuity of a Function

The function ...

Question

The function f(x) defined as f(x) = $\sqrt{(x - 4)^{2}}$

continuous but not differentiable $\forall x ϵ R$

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continuous and differentiable $\forall x ϵ R$

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not continuous at x = 4

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continuous only for $x \geq 4$

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Solution

The correct option is A
continuous but not differentiable $\forall x ϵ R$

$f (x) = \sqrt{(x - 4)^{2}} = | x - 4 | | x - 4 | i s c o n t i n u o u s \forall x ϵ R$
It is not differntiable at x = 4

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The function f(x) defined as f(x) = √(x−4)2

The correct option is A continuous but not differentiable ∀ x ϵ R f(x)=√(x−4)2=|x−4||x−4| is continuous ∀ x ϵ R It is not differntiable at x = 4

The function f(x) defined as f(x) = $\sqrt{(x - 4)^{2}}$

The correct option is A
continuous but not differentiable $\forall x ϵ R$

$f (x) = \sqrt{(x - 4)^{2}} = | x - 4 | | x - 4 | i s c o n t i n u o u s \forall x ϵ R$
It is not differntiable at x = 4