SOLUTION: Find the domain of the function f(x)=1 _____ x-4

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Question 139504: Find the domain of the function
f(x)=1
_____
x-4
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%281%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





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:

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-6%2C+14%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 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