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

 Mar 7, 2024
 #1
avatar+128794 
+2

Simplify as

 

sqrt [ -3x^2 - x + 6  ]

 

-3x^2 - x + 6 =  0

 

3x^2 + x - 6   = 0

 

x  =   [ -1 - sqrt 73 ] / 6   ≈ -1.59     and  x = [ 1 +sqrt 73  ] / 6 ≈ 1.26

 

The root will be real when x =  [  (-1- sqrt 73)/6  , (-1 +sqrt 73)/6 ]  = the domain

 

cool cool cool

 Mar 7, 2024

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