How do you find the domain and range ofsquare root functions?

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

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

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- Sep 30th 2008, 08:29 PMmagentaritaDomain 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} - Sep 30th 2008, 09:02 PMJameson
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.

- Sep 30th 2008, 10:43 PMmr fantastic
- Oct 1st 2008, 04:24 PMmagentaritayes but......
- Oct 1st 2008, 05:36 PMKrizalid
Well, it's not that hard to find the "why."

Let's use our brain: having $\displaystyle f(x)=\sqrt x.$ For what values of $\displaystyle x,$ $\displaystyle \sqrt x$ is well defined? Yes, we require that $\displaystyle x\ge0,$ 'cause $\displaystyle x$ 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 $\displaystyle x\ge0.$

Now, by applyin' this to your problems, you'll see this does make sense. - Oct 2nd 2008, 03:01 AMmagentaritaok