What is the domain of the function #(x-2)/sqrt(x^2-8x+12)# ?
2 Answers
Explanation:
Given:
#(x-2)/sqrt(x^2-8x+12)#
This function is well defined when the radicand is positive.
We find:
#x^2-8x+12 = (x-2)(x-6)#
which is
So the domain is
The domain is
Explanation:
We have a couple of conditions that need to be addressed:
•When will the value under the
#√# be inferior to#0# ?
•When will the denominator equal#0# ?
For the function to be defined on
#sqrt(x^2 - 8x + 12) ≥ 0#
Solve as an equation
#x^2 - 8x + 12 =0#
#(x - 6)(x - 2) =0#
#x= 6 or 2#
We now select test points.
Test point
Therefore, the intervals that work are
Our domain becomes
Hopefully this helps!