SOLUTION: Please help me find the domain and write BOTH the set-builder and the interval notation for f(x)=x^2-3x-4 over x^2-18x+77. Thank you

Question 107521This question is from textbook Intermediate Algebra
: Please help me find the domain and write BOTH the set-builder and the interval notation for f(x)=x^2-3x-4 over x^2-18x+77. Thank you This question is from textbook Intermediate Algebra

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.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for x in each case

So our solutions are or

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

So our domain is:

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

So our domain looks like this in interval notation

note: remember, the parenthesis excludes 7 and 11 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 and (which is represented by the open circles).
This graphically represents our domain in which x can be any number except x cannot equal 7 or 11

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