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What real values of x are not in the domain of $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x - 10|}$?

 
 Oct 13, 2021
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Both of those absolute values will be great or equal to zero.

The only time the denominator will be zero is when both absolute expresssions are = 0

 

so   

\(x^2+3x-4 =0\qquad and \qquad   x^2+9x-10 = 0\\ (x+4)(x-1)=0 \qquad and \qquad   (x+10)(x-1) = 0\\ so \qquad x=1 \)

 

the only real value of x are not in the domain of  f(x) is 1

 

 

Here is the graph:

 
 Oct 13, 2021

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