SOLUTION: i did this problem i just want to see if i did it right.. what is the domain? 7-X/5x^2-18x-8 thanks for your help angela

Question 132287This question is from textbook introductory and intermediate algebra
: i did this problem i just want to see if i did it right..

what is the domain?
7-X/5x^2-18x-8

thanks for your help
angela This question is from textbook introductory and 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 and 4 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 or 4

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