State True or False for the statements If f is continuous on its domain D, then |f| is also continuous on D.

Question

Philoid · Accepted Answer

True

Given that, f is continuous on its domain D.

Let a be an arbitrary real number in D. Then f is continuous at a.

⇒

Now,

⇒ [∵ |f|(x) = |f(x)| ]

⇒

∴ |f| is continuous at x=a.

Since a is an arbitrary point in D. Therefore |f| is continuous in D.