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I am practicing for my ACT exams, but I cannot get this question right on the practice test. First I thought H, and then F, but I am having trouble with it.

Suppose the following:

f(x)=(3x(x-1))/(x^2-3x+2), for x cannot equal 1 or 2.

f(1)=-3

f(2)=4

This means that f(x) is continuous at which of the following:

F) except at x=1

G) except at x=2

H) except at x=1 or 2

I) except at x=0, 1 or 2

J) at each real number

f(x) is continuous at x=1 because

1 is part of the domain

f(1) = -3

limit of 3x(x-1)/(x˛-3x+2) as x approaches 1 = -3 = f(1)

Limit of 3x(x-1)/(x˛-3x+2) as x approaches 2 from the left is -∞.

The limit of 3x(x-1)/(x˛-3x+2) as x approaches 2 from the right is ∞.

However, f(2) ≠ -∞ or ∞. The function is discontinuous at x=2.

=====

Sorry, I must retract this answer—may have made a mistake regarding the limit as the function approaches 2.

Will check my work and update.

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