+0  
 
0
7
1
avatar+1351 

Find the domain of the function f(x)=\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}}.

 Apr 3, 2024
 #1
avatar+128794 
+1

\(\sqrt{1-\sqrt{2+\sqrt{3+\sqrt{x}}}} \)

 

 

Note   that  even if x =  0   (as small as it  can  be),,,we have

 

1 - sqrt [ 2 + sqrt (3) ]   which is less than   0......so the quantity under the radical isn't real

 

If x >  0     then    sqrt [ 2 + sqrt (3 + sqrt (x)) ]    will still be >1  which makes the quantity under the radical still < 0] 

 

So.....this  can't have a domain of real numbers

 

cool cool cool

 Apr 4, 2024

1 Online Users