SOLUTION: I'm not sure if I am solving this problem correctly. The problem is find the domain h(x)=x+3/x-4 This is my work so far x-4=0 x=4

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Question 102473: I'm not sure if I am solving this problem correctly. The problem is find the domain h(x)=x+3/x-4
This is my work so far x-4=0
x=4
(-4,0)U(0,4]
Can someone tell me if this is right.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

h%28x%29=%28x%2B3%29%2F%28x-4%29 Start with the given function


x-4=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%2B4Add 4 to both sides


x=4 Combine like terms on the right side

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Answer:
So our answer is x=4



Since x=4 makes the denominator equal to zero, this means we must exclude x=4 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E4

So our domain looks like this in interval notation


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

Notice we have a continuous line until we get to the hole at x=4 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 4