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# Domain and Range

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

Jul 22, 2018

#1
+95966
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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

Jul 23, 2018