What is the domain of the function y=ln(x^2-3x+2) ?

In the domain of definition of the given function there
are found all the admissible values of x for the logarithmic function to
exist.

We'll impose the conditions 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 = 1

The expression is
positive over the intervals:

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

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

The reunion of intervals
represents the domain of definition of the given function  f(x) = ln (x^2 - 3x
+ 2).