If f(x) = | log|x||, then

Question

If f(x) = | log|x||, then (A) f(x) is continuous and differentiable for all x in its domain (B) f(x) is continuous for all x in its domain but not differentiable at x = ± 1 (C) f(x) is neither continuous nor differentiable at x = ± 1 (D) None of the above

Tardigrade Admin · Accepted Answer

From the graph of f(x ) = | log|x|| it is clear that f(x) is everywhere continuous but not differentiable at x = ± 1

Q. If $f (x) = ∣ lo g ∣ x ∣∣$ , then

$f (x)$ is continuous and differentiable for all $x$ in its domain

$f (x)$ is continuous for all $x$ in its domain but not differentiable at $x = \pm 1$

$f (x)$ is neither continuous nor differentiable at $x = \pm 1$

None of the above

From the graph of $f (x) = ∣ lo g ∣ x ∣∣$ it is clear that $f (x)$ is everywhere continuous but not differentiable at $x = \pm 1$

Q. If f(x)=∣log∣x∣∣, then

f(x) is continuous and differentiable for all x in its domain

f(x) is continuous for all x in its domain but not differentiable at x=±1

f(x) is neither continuous nor differentiable at x=±1