+0  
 
-1
28
1
avatar+527 

Find the domain of the function $f(x) = \sqrt{6-x-x^2-2x^2}$.

 Aug 27, 2023
 #1
avatar+126607 
+1

Simplify as

 

sqrt [ -3x^2 - x + 6 ] 

 

The expression under the root  must be  ≥ 0   (we can't take the sq rt  of a  negative)

 

So

 

-3x^2 - x +  6  ≥  0

 

This is a  parabola that opens  downward......all we have to  do is to  find the  roots....the domain will lie  between these roots an also include them....so...

 

-3x^2  - x  + 6 = 0         multiply through by -1

 

3x^2 + x - 6 =  0

 

By the quadratic formula

 

x =   [ -1 - sqrt [ 1^2 - 4*3* -6 ]/ [ 2 *3 ] =   [ -1 - sqrt ( 73 ) ] / 6

and

x =  [ -1 + sqrt (73) ]  6

 

So....the domain  is

 

[    (-1 -sqrt 73) / 6  ,  (-1 + sqrt 73) / 6    ] 

 

cool cool cool

 Aug 27, 2023

2 Online Users

avatar