# Help if you can: Domain of the function sqrt(x(x-7)) in interval notation. Can you show the steps as well please :)?

Reference: Math.com

The domain of a function is the set of all possible x values which will make the function "work" and will output real y-values.

When finding the domain, remember:

•The denominator (bottom) of a fraction cannot be zero
•The values under a square root sign must be positive

For this function if you have a negative square root, the result is an imaginary number.  So the domain is everywhere that x(x -7) is not zero, and not negative.

The easy one first    When x = 7, then the function is x(0)  - No good.  So we know that at x = 7, the function doesn't work, and 7 is therefore excluded.

If x = 0, then the function fails again, so @ x = 0, the function doesn't work and 0 is therefore excluded.

Now check a number between 0 and 7 to see if any of these numbers work.  Say 1

1(1-7) ends up with -7, and square root is imaginary.  Doesn't work.

Try lower than 0 say -1

-1(-1-7) = -1(-8) = 8  O.K.  It works.

So the domain is all numbers less than 0, and greater than 7
thanked the writer.
Oddman commented
√0 = 0, so the end points of the intervals can be included in the solution set.