In this question: The domain of the function h(x) = sqrt(25-x^2) + sqrt(-(x-2) is an interval of what width?

I think the domain is: [2, -5], so in total, 8 terms satisfy the domain, so is the with 8? Because apparently it's not...can someone explain this to me?

Guest Apr 25, 2018

#1**+1 **

√[25 - x^2 ] + √[ - ( x - 2) ] =

√[25 - x^2 ] + √ [2 - x ]

The domain for the first function is [ -5, 5 ]

The domain for the second function is ( - infinity, 2]

Because we must take the most restrictive interval, this is [ -5, 2 ]

So....the width of the interval is 7 units [ 8 integers ]

So the graph, here : https://www.desmos.com/calculator/ioiruyyh4v

CPhill
Apr 25, 2018