APFIVE Continuity and Differentiability of a Piecewise Function
Let $$g$$ be the function defined by $$g(x) = \begin{cases} x^2 & \text{if } x \leq 2 \\ 3x - 2 & \text{if } x > 2 \end{cases}$$. Which of the following statements about $$g$$ is true?
A
$$g$$ is differentiable but not continuous at $$x = 2$$.
B
$$g$$ is continuous but not differentiable at $$x = 2$$.
C
$$g$$ is defined but neither continuous nor differentiable at $$x = 2$$.
D
$$g$$ is continuous and differentiable at $$x = 2$$.
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