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Function f(x) = |cos x| is

(A) Continuous only in [0, π/2]
(B) Continuous only in [−π/2, π/2]
(C) Continuous only in [−π, π]
(D) None

1 Answer

Best answer
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Below are the graphs for f(x) = cos x  & f(x) = |cos x|      Clearly both are continuous. every where.

If you want to do manually,

f(x) = |cos x|
f(x) =  cos x  when  cos x > 0  i.e when x is in between  [−π/2, π/2]  
f(x) =  −cos x when  cos x <0  ie  when x is in between  [π/2, −π/2]

Now do (A) (B) (C)
You will see all are continuous.
Answer is D because of the word "ONLY".
It is continuous every where.

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