Find all the points of discontinuity of the f | vedclass

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(C) The function $f$ is defined as:$f(x) = \begin{cases} x + 2, & 	ext{if } x  1 \end{cases}$F

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$x=1$

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(C) The function $f$ is defined as:$f(x) = \begin{cases} x + 2, & 	ext{if } x  1 \end{cases}$For any $x 
eq 1$,the function is a polynomial,which is continuous. We only need to check the continuity at $x = 1$.The left-hand limit $(LHL)$ at $x = 1$ is:$\lim_{x 	o 1^-} f(x) = \lim_{x 	o 1^-} (x + 2) = 1 + 2 = 3$The right-hand limit $(RHL)$ at $x = 1$ is:$\lim_{x 	o 1^+} f(x) = \lim_{x 	o 1^+} (x - 2) = 1 - 2 = -1$The value of the function at $x = 1$ is $f(1) = 0$.Since $\lim_{x 	o 1^-} f(x) 
eq \lim_{x 	o 1^+} f(x)$,the limit does not exist at $x = 1$. Therefore,the function is discontinuous at $x = 1$.

Find all the points of discontinuity of the function $f$ defined by
$f(x) = \begin{cases} x + 2, & \text{if } x < 1 \\ 0, & \text{if } x = 1 \\ x - 2, & \text{if } x > 1 \end{cases}$

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Find all the points of discontinuity of the function $f$ defined by$f(x) = \begin{cases} x + 2, & \text{if } x < 1 \\ 0, & \text{if } x = 1 \\ x - 2, & \text{if } x > 1 \end{cases}$