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Find the domain of the function.

$ g(t) = \sqrt{3 - t} - \sqrt{2 + t} $

$-2 \leq t \leq 3$

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Missouri State University

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

we want to find the domain of this function. And remember that domain would be the set of rial number inputs that would yield rial number outputs. And so, when we're looking at square root functions, we need to have the square root of a non negative number square root of zero or the square root of a positive will yield a really result, but the square root of a negative number will yield an imaginary non real result. And so we need three minus T to be greater than or equal to zero. And we need to plus T to be greater than or equal to zero to get real outputs. So let's solve this compound inequality. We can subtract three from both sides of the 1st 1 and we get the opposite of tea is greater than or equal to negative. Three. Divide both sides by negative one. And don't forget to reverse the inequality when you do that, so tea is less than or equal to three. And for the other one, we can subtract two from both sides, and we get T is greater than or equal to negative two. So putting these together this is and so we want the intersection of these two sets, so this would be negative. Two is less than or equal to. Tea is less than or equal to three. And if you want to write that using interval notation, you would have the interval from negative 2 to 3 like that.