see in the graph any where any certain point has two values no and any point function value is not defined no so the function is continuous this is a example of discontinuous https://en.wikipedia.org/wiki/Classification_of_discontinuities#/media/File:Discontinuity_jump.eps.png at x0 different values are there
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.
@srestha Source of this question is Virtual Gate. Right ?