+0  
 
-1
63
1
avatar+753 

What real values of $x$ are not in the domain of \(f(x)=\frac{1}{|x^2+3x-4|+|x^2+9x+20|}\)?

Lightning  Jul 22, 2018
 #1
avatar+89953 
+1

1 /  (  l x^2 + 3x  - 4 l + l x^2 + 9x + 20 l )

 

Note that we  cannot have   x^2 + 3x - 4    and x^2 + 9x + 20    both equaling 0 at the same time

 

So.....factoring   x^2 + 3x  -  4  and setting it to 0, we get that

(x + 4) ( x - 1)    = 0

Setting each factor to  0 and solving for x, we get that   x = -4   or  x =  1

 

Similarly....factoring x^2 + 9x + 20   and setting this to  0, we get that

(x + 4) ( x + 5)    =  0

Setting each factor to 0 and solving for  x, we get that x = -4 or  x  = -5

 

So...it appears the the  real  value that makes both parts of the denominator  = 0  is when x  = -4

 

See the graph, here : https://www.desmos.com/calculator/ssgeajyewr

 

 

cool cool cool

CPhill  Jul 23, 2018

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