What are the removable and non-removable discontinuities, if any, of #f(x)=(x^2+4x+2)/(x^2-2x)#?

1 Answer
Jim H
Sep 23, 2016

The function has non-removable discontinuities at #0# and #2#. It has no other discontinuities.

Explanation:

The function is undefined for #x=0# and for #x=2#, so it has discontinuities only at those two numbers. (Rational functions are continuous on their domains, so #f#.)

#lim_(xrarr0)f(x)# and #lim_(xrarr2)f(x)# do not exist, so te discontinuities cannot be removed.

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