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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.
Subtract 25 from both sides.
Take the square root of both sides.
Factor
into
Replace
with "i"
or
Take the square root of 25 to get 5 or -5
Since the values
or
make the denominator zero, this means that there are no real x values that make the denominator zero (since
and
are both complex).
So you can plug in any real number for x and you'll get a result for f(x).
If that doesn't make any sense to you, then try to think of it like this:
is
always positive. So there are no real values that make
true. That's why the domain includes all real numbers.
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Answer:
So the domain of the function in set-builder notation is:
In plain English, this reads: x is the set of all real numbers (In other words, x can be
any number)
Also, in interval notation, the domain is:
)
