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The domain of the function h(x) = \sqrt{25-x^2}+\sqrt{-(x-2)}+\sqrt{x} is an interval of what width?

 Jun 7, 2022
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\( h(x) = \sqrt{25-x^2}+\sqrt{-(x-2)}+\sqrt{x}\)

 

h(x)  =  sqrt (25 - x^2)  + sqrt (2 - x) +  sqrt (x)

 

The first term  has a domain  of   [ -5 , 5 ]

 

The second term has a domain of   ( -inf , 2]

 

The third term has a domain of  [ 0 , inf)

 

The most restrictive interval   is   [ 0 ,2 ]

 

So....the width of the domain interval  =  2

 

cool cool cool

 Jun 7, 2022
edited by CPhill  Jun 7, 2022

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