Determining where a function is continuous, Epsilon-Delta Continuity Problem

Determine where the function f(x) = x + [|x^2|] - [|x|] is continuous

I don't understand how to work this problem. Can someone show and explain how to solve this problem in detail? I've asked for help on this problem before but I still don't understand it.

The function is continuous everywhere but 0. I don't understand how to get that answer or what method is used to arrive to that conclusion.

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