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