If f(x) = begin{cases} 1 + x, & text{when } x | vedclass

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(A) To check the continuity of $f(x)$ at $x = 2$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 2$.$1$. Left-h

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$f(x)$ is continuous at $x = 2$

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(A) To check the continuity of $f(x)$ at $x = 2$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 2$.$1$. Left-hand limit: $\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^-} (1 + x) = 1 + 2 = 3$.$2$. Right-hand limit: $\lim_{x 	o 2^+} f(x) = \lim_{x 	o 2^+} (5 - x) = 5 - 2 = 3$.$3$. Value of the function: $f(2) = 1 + 2 = 3$.Since $\lim_{x 	o 2^-} f(x) = \lim_{x 	o 2^+} f(x) = f(2) = 3$,the function $f(x)$ is continuous at $x = 2$.

If $f(x) = \begin{cases} 1 + x, & \text{when } x \le 2 \\ 5 - x, & \text{when } x > 2 \end{cases}$,then which of the following is true?

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