We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
-1
195
1
avatar+1055 

Compute the domain of the real-valued function \( f(x)=\sqrt{1-\sqrt{2-\sqrt{x}}}.\)

 Jul 24, 2018
 #1
avatar+99604 
+1

We can solve this by inspection

 

Note that when  x = 1   the expression  under the entire radical  is 0

And x cannot be smaller than this   (note if it were, for example, 0,   1 - √2  under the radical would be  negative

 

And  x  cannot be  larger than 4   because    [2 - √x ]   would result in a negative quantity under a radical

 

So...the domain  is  [ 1, 4 ]

 

Here's a graph : https://www.desmos.com/calculator/xxzra4wyai

 

cool cool cool

 Jul 24, 2018
edited by CPhill  Jul 24, 2018

14 Online Users

avatar
avatar
avatar