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 ->  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

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

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(21667) 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

--------------------------------------------------------------
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:

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-7%2C+13%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 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