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# Domain

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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