# Does the function # f(x) = x/(|x|-3)# have any discontinuities?

##### 1 Answer

May 12, 2017

There are discontinuities when

#### Explanation:

We have:

# f(x) = x/(|x|-3) #

Her is a graph of the function. At first appearance, it would look as through

graph{x/(|x|-3) [-10, 10, -10, 10]}

Both the numerator and denominator are continuous functions in their own right. The combination leading to the definition of

ie there could only be a discontinuity if

# |x|-3 = 0 => |x| = 3 => x=+-3#

Hence, There are discontinuities when