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).
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