Determine the domain of definition of the function y=ln(x^2-3x+2) .

In the domain of definition of the given function has to
be all the values of x for the logarithmic function to
exist.

We'll impose the constraint for the logarithmic
function to exist: the argument of logarithmic function has to be
positive.

x^2 - 3x + 2 >
0

We'll compute the roots of the
expression:

x^2 - 3x + 2 =
0

We'll apply the quadratic
formula:

x1 = [3 +sqrt(9 -
8)]/2

x1 = (3+1)/2

x1 =
2

x2 = (3-1)/2

x2 =
1

The expression is positive over the
intervals:

(-infinite , 1) U (2 ,
+infinite)

So, the logarithmic function is
defined for values of x that belong to the intervals (-infinite , 1) U (2 ,
+infinite).

The domain of
definition of the given function y=ln(x^2-3x+2) is the reunion of intervals (-infinite ,
1) U (2 , +infinite).