Answer :
Using the continuity concept, it is found that f(2) = 4 would make the extended function continuous at x=2.
What is the continuity concept?
A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
Researching this problem on the internet, from the graph of the function, we get that the lateral limits are given as follows:
[tex]\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2^+} f(x) = 4[/tex]
Hence f(2) = 4 would make the extended function continuous at x=2.
More can be learned about the continuity concept at https://brainly.com/question/24637240
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