SOLUTION: Find the domain of y=1/(x+1)(x-3) Write the domain in interval notation

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Question 105759: Find the domain of y=1/(x+1)(x-3)
Write the domain in interval notation
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=%281%29%2F%28%28x-3%29%28x%2B1%29%29 Start with the given function


%28x-3%29%28x%2B1%29=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.




Now set each factor equal to zero:

x-3=0 or x%2B1=0

x=3 or x=-1 Now solve for x in each case


So our solutions are x=3 or x=-1



Since x=-1 and x=3 make the denominator equal to zero, this means we must exclude x=-1 and 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%3E-1 or x%3C%3E3

So our domain looks like this in interval notation


note: remember, the parenthesis excludes -1 and 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 values represented by open circles

Notice we have a continuous line until we get to the holes at x=-1 and x=3 (which is represented by the open circles).
This graphically represents our domain in which x can be any number except x cannot equal -1 or 3