.
Such function DOES NOT exist.
Therefore, the requested example CAN NOT be provided.
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More detailed explanation.
The statement [ lim x --> 4 f(x) = 10 ] means, by default, that the function f(x) is CONTINUOUS at x= 4.
Therefore, when you request to give
an example of a function so that limxβ4 π(π₯) = 10 but f(x) is discontinuous at x = 4
your request DOES NOT MAKE SENSE.