SOLUTION: I need the domain of the following problem: {{{g(x)=5x/x^2+25}}} Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should

Question 151704: I need the domain of the following problem:
Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should be able to work it.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.

-------------------------------------------------------------

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:

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