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Topology

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Continuity of Piecewise Functions

TOPO-Q6VABF

Suppose that

$$f(x):=\left\{\begin{matrix}x^2&\text{ if }x\le 2 \\\ b-x&\text{ if }x>2\end{matrix}\right.$$

For what value of $b\in\mathbb R$ is $f:\mathbb R\rightarrow\mathbb R$ continuous? Assume the standard topology on $\mathbb R$.

A

4

B

5

C

6

D

7

E

8