SOLUTION: Find the domain? K(x) = x-2/x-3 - write the answer in interval notation.. now on this proplem i know the asnwer is (- infinity, 3) U (3, infinity) but how do i figure th

Question 99371: Find the domain?
K(x) = x-2/x-3 - write the answer in interval notation..

now on this proplem i know the asnwer is (- infinity, 3) U (3, infinity)
but how do i figure that out??
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given function

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.

Add 3 to both sides

Combine like terms on the right side

--------------------------------------------------------------
Answer:
So our answer is

Since makes the denominator equal to zero, this means we must exclude from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except

So our domain looks like this in interval notation

note: remember, the parenthesis excludes 3 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 3

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