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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.
Add 5 to both sides
Combine like terms on the right side
Since
makes the denominator equal to zero, this means we must exclude
from our domain
So our domain is:
which in plain English reads: x is the set of all real numbers except x CANNOT equal
So our domain looks like this in interval notation
\cup\left(5,\infty \right))
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
(which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal 5
