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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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

f%28x%29=%28x%5E2-3x-4%29%2F%28x%5E2-18x%2B77%29 Start with the given function


x%5E2-18x%2B77=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.




%28x-11%29%28x-7%29=0 Factor the left side (note: if you need help with factoring, check out this solver)




Now set each factor equal to zero:

x-11=0 or x-7=0

x=11 or x=7 Now solve for x in each case


So our solutions are x=11 or x=7



Since x=7 and x=11 make the denominator equal to zero, this means we must exclude x=7 and x=11 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E7 or x%3C%3E11

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 x=7 and x=11 (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