9. Find all points of discontinuity of f, where f is defined by

f (x) = \left\{\begin{matrix} \frac{x }{|x|} & if \: \: x < 0\\ -1 & if x \geq 0 \end{matrix}\right.
 

Answers (1)

Given function is 
f (x) = \left\{\begin{matrix} \frac{x }{|x|} & if \: \: x < 0\\ -1 & if x \geq 0 \end{matrix}\right.
if x < 0 , f (x) =\frac{x }{|x|} = \frac{x}{-(x)} = -1
Now, for any value of x, the value of our function is -1 
Therefore, the given function is continuous for each and every value of x 
Hence, no point of discontinuity

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