What is the domain of definition of the function f(x) = log 2 (x^2 - 5x + 6) ?

The domain of definition of the given function contains
the admissible 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 - 5x + 6 >
0

We'll compute the roots of the
expression:

x^2 - 5x + 6 =
0

We'll apply the quadratic
formula:

x1 = [5 +/- sqrt(25 -
24)]/2

x1 = (5+1)/2

x1 =
3

x2 = 2

The expression is
positive over the intervals:

(-infinite , 2) U (3 ,
+infinite)

So, the logarithmic function is
defined for values of x that belong to the intervals (-infinite , 2) U (3 ,
+infinite).

The reunion of
intervals represents the domain of definition of the given function  f(x) = log 2 (x^2 -
5x + 6).