The function f(x) = |x| + frac{|x|}{x} is | vedclass

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(C) The function is defined as $f(x) = |x| + \frac{|x|}{x}$.First,consider the term $|x|$. The function $g(x) = |x|$ is continuous for all real number

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Discontinuous at the origin because $\frac{|x|}{x}$ is discontinuous there

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(C) The function is defined as $f(x) = |x| + \frac{|x|}{x}$.First,consider the term $|x|$. The function $g(x) = |x|$ is continuous for all real numbers,including $x = 0$.Second,consider the term $h(x) = \frac{|x|}{x}$. For $x > 0$,$h(x) = \frac{x}{x} = 1$. For $x Since the left-hand limit $\lim_{x 	o 0^-} h(x) = -1$ and the right-hand limit $\lim_{x 	o 0^+} h(x) = 1$ are not equal,the function $h(x)$ is discontinuous at $x = 0$.Since the sum of a continuous function and a discontinuous function is discontinuous,$f(x) = |x| + \frac{|x|}{x}$ is discontinuous at $x = 0$ due to the term $\frac{|x|}{x}$.

The function $f(x) = |x| + \frac{|x|}{x}$ is

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