Q103 of 107 Page 107

State True or False for the statements

If f is continuous on its domain D, then |f| is also continuous on D.

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.


More from this chapter

All 107 →
101

Fill in the blanks in each of the

For the curve is _______.

 102

State True or False for the statements

Rolle’s theorem is applicable for the function f(x) = |x – 1| in [0, 2].

 104

State True or False for the statements

The composition of two continuous functions is a continuous function.

 105

State True or False for the statements

Trigonometric and inverse–trigonometric functions are differentiable in their respective domain.