SOLUTION: consider the function t defined by t(z)=z^2-z-6/z^2+z-12 a. determine the location of the removable discontinuity of function t. b. show that t has an essential discontinuity a

Question 308831: consider the function t defined by t(z)=z^2-z-6/z^2+z-12
a. determine the location of the removable discontinuity of function t.
b. show that t has an essential discontinuity at z=-4.
c. find the domain of this fuction.
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
a.

t(z)=(z^2-z-6)/(z^2+z-12)

t(z)=((z-3)(z+2))/((z-3)(z+4))

t(z)=(z+2)/(z+4)

removable discont at z=3

b.

discont at z=-4 since z+4 is denominator

c.

Domain: set of all real numbers but z =/= 3 or z =/= -4
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