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Numerade Educator

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Problem 37 Hard Difficulty

Find the domain of the function.

$ F(p) = \sqrt{2 - \sqrt{p}} $

Answer

interval $[0,4]$

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Video Transcript

we're going to find the domain of this function. So remember that the domain would be the set of rial number inputs that would yield rial number outputs. And so, when you're looking at a square root function in particular, you want to make sure that you're taking the square root of a non negative number either the square root of zero or the square root of pot A positive because we know that the square root of a negative is non riel. So we have two things to consider. One is the inside square root. We need the square root of P. We need what is inside the square root of P. So we need P to be greater than or equal to zero for that square root to have a real output. Okay, but also we have what's inside the big square root you could say so we need to minus square root p to be greater than or equal to zero. That means we need to to be greater than or equal to square root p or, if I flip it around square root p to be less than or equal to two. Now we already know that Pius positive or zero from the other inequality. So if we square both sides of this, we need P to be less than or equal to four. We need both of things, these things to be true. So this is an and statement. And so if we put that in interval notation, it looks like this. The domain is the interval from 0 to 4 close brackets to show where including the endpoints. If we want to put it in set notation, we can say zero is less than or equal to P is less than or equal to four. These statements are equivalent.