SOLUTION: Can someone please explain to me how to do this problem? Find the domain of the rational expression. f(x)=3x+1 _____ x-5 Thanks

Algebra ->  Functions -> SOLUTION: Can someone please explain to me how to do this problem? Find the domain of the rational expression. f(x)=3x+1 _____ x-5 Thanks      Log On


   

Question 165631: Can someone please explain to me how to do this problem?
Find the domain of the rational expression.
f(x)=3x+1
_____
x-5
Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%283x%2B1%29%2F%28x-5%29 Start with the given function


x-5=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%2B5Add 5 to both sides


x=5 Combine like terms on the right side





Since x=5 makes the denominator equal to zero, this means we must exclude x=5 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x CANNOT equal 5

So our domain looks like this in interval notation


note: remember, the parenthesis excludes 5 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 value represented by open circle

Notice we have a continuous line until we get to the hole at x=5 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 5