What are the removable and non-removable discontinuities, if any, of #f(x)=(2x^2+4x-6) / (x-1)#?

1 Answer
Jim H · mason m
Feb 22, 2017

There is a removable discontinuity at #x=1#. That is the only discontinuity.

Explanation:

#f# is a rational function. Rational functions are continuous on their domains. The domain of #f# is #(-oo,1) uu (1,oo)#

So #f# is continuous except at #x=1#

#lim_(xrarr1) f(x) = lim_(xrarr1)((2x+6)(x-1))/(x-1)#

#=lim_(xrarr1)(2x+6)#

# = 2+6 = 8#

Because the limit exists, the discontinuity is removable.

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