Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

True or False: If f is continuous on its domain D ,then | f | is also continuous on D.

Can you answer this question?

1 Answer

0 votes
  • A function is said to be continuous on an open interval $(a,b)$ if it is continuous at every point on the interval $(a,b)$.$\mid f\mid$ is defined as $\mid f\mid(x)=\mid f(x)\mid$
Let $'a'$ be an arbitrary real number in domain $D$.Then $f$ is continuous at $a$.
Therefore $\lim\limits_{\large x\to a}f(x)=f(a)$
Now $\lim\limits_{\large x\to a}\mid f\mid(x)=\lim\limits_{\large x\to a}\mid f(x)\mid$
$\Rightarrow \mid f(a)\mid=\mid f\mid(a)$
Therefore $\mid f\mid$ is continuous at $x=a$
Therefore it is a True statement.
answered Jul 5, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App