+1242 What real values of $x$ are not in the domain of \(f(x)=\frac{1}{|x^2+3x-4|+|x^2+9x+20|}\)?
+128406 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
