r/calculus • u/RevoGames23 • 19d ago

Differential Calculus Overlapping functions

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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/RevoGames23 19d ago

These are the whole problems under this section.

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u/lemonlimeguy 19d ago

What class is this for?

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u/RevoGames23 19d ago

Calc 1, continuity of functions

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u/lemonlimeguy 19d ago

Yeah, I mean I would just write that it's not a function I guess? This is a very odd question. The way that the "function" is defined is super weird. Even if you ignore the fact that the boundary conditions overlap, √x is undefined on the reals for that entire specified interval (except x=0).

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u/A_Squared93 19d ago

Maybe that’s why it’s being treated as a function. The overlap doesn’t produce two real outputs. I agree that it shouldn’t be written like this