Question

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

• A. continuous but not differentiable $\forall xϵR$
• B. continuous and differentiable $\forall xϵR$
• C. not continuous at x = 4
• D. continuous only for $x\ge 4$

Answer 1

The correct option is A

continuous but not differentiable $\forall xϵR$

$f\left(x\right)=\sqrt{(x-4{)}^2}=|x-4||x-4|iscontinuous\forall xϵR$
It is not differntiable at x = 4