Suppose f(x)=3x(x-1)/x²-3x+2 for x≠1,2,f(1)= -3,f(2)=4 then f(x) is continuous

a) except at x=1
b) except at x=2
c) except at x =1 or 2
d) except at x= 0,1, or 2
e) at each real number

1 answer

x²-3x+2 = (x-1) (x-2)
so your function is
f(x)=3x/(x-2) for x≠1,2,f(1)= -3,f(2)=4
yes f(1) = -3 , no problem with continuous there if f(1) given as -3
but at x = 2 the thing blows up as we approach x = 2 and saying that f(2)= 4 does not help.