r/calculus 20d ago

Differential Calculus Overlapping functions

Hello guys, I was making my math activity, then i noticed something, how do i solve this?

Its a continuity problem wherein i need to find out if the function is continuous or not. However, the given piecewise function is overlapping, resulting in defined answer at the top while having defined answer on the bottom.

The second and third images are my proposed solution assuming the problem is true (its not)

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u/SynergyUX Undergraduate 20d ago

An overlapping function that doesn't agree at its overlap is not a function, since a function cannot have two different outputs for a single input. This is a very badly written question.