# 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 #1: x = 1#**

Therefore, the intervals that work are

Our domain becomes

Hopefully this helps!