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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

K%28x%29=%28x-2%29%2F%28x-3%29 Start with the given function


x-3=0 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.



x=0%2B3Add 3 to both sides


x=3 Combine like terms on the right side

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Answer:
So our answer is x=3



Since x=3 makes the denominator equal to zero, this means we must exclude x=3 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E3

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 x=3 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 3