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Question

Find all the points of discontinuity of f(x) defined by f(x)=|x|-|x+1|.

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Solution

Let g(x) =|x| and h(x) = |x+1|

Now, g(x) =|x| is the absolute valued function, so it is continuous function for all x ϵR

h(x)=|x|+1 is the absolute valued function, so it is a continuous function for all x ϵR

Since, g(x) and h(x) are both continuous functions for all x ϵR so, difference of two continuous function is a continuous function for all x ϵR
Thus, f(x) =con(x2) is a continuous function at all points.

Hence, there is no point at which f(x) is discontinuous.


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