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Sir, if f(x) is continuous, then |f(|x|)| is also continuous? How?

Asked by Seshadri S 30th March 2013, 5:33 PM
Answered by Expert
Answer:
If f(x) is continuous, that means that it is continuous for both positive and negative values of x. 
 
Now, considering f(|x|) -- the value of this function will only correspond to the values of f(x) for x>=0. And since, f(x) is continuous for all values of x as well as at x =0, hence, f(|x|) will also be continuous for all values of x. 
Answered by Expert 30th March 2013, 6:13 PM
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