Thread: Domain of Square Root Function

How do you find the domain and range of square root functions?

(1) Find the domain of y = sqrt{2x + 3}

(2) Find the domain of f(x) = sqrt{2x - x^2}

Well since we're dealing with real numbers, we aren't allowed to take the square-root of a negative number. So find out for what x-values the expression inside the square-root is less than 0.

Originally Posted by Jameson

Well since we're dealing with real numbers, we aren't allowed to take the square-root of a negative number. So find out for what x-values the expression inside the square-root is less than 0.

Just to expand a bit, the domains are given by the solution to the following inequations:

(1) Solve .

(2) Solve .

Originally Posted by mr fantastic

Just to expand a bit, the domains are given by the solution to the following inequations:

(1) Solve .

(2) Solve .

Yes, but why? I am looking for the why of things not just how to find the answer.

Well, it's not that hard to find the "why."

Let's use our brain: having For what values of is well defined? Yes, we require that 'cause can be zero, or positive, but it can't be negative, since square roots of negative numbers don't belong to the Real numbers, that's why we require

Now, by applyin' this to your problems, you'll see this does make sense.

Originally Posted by Krizalid

Well, it's not that hard to find the "why."

Let's use our brain: having For what values of is well defined? Yes, we require that 'cause can be zero, or positive, but it can't be negative, since square roots of negative numbers don't belong to the Real numbers, that's why we require

Now, by applyin' this to your problems, you'll see this does make sense.

ok...now I get it.