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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 12, 2019

#1
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The only values not in the domain are those that make the denominator zero.

Both terms are positive so they must both simultaneously be zero.

$$x^2 + 3x-4 = (x+4)(x-1)\\ x^2+9x+20 = (x+4)(x+5)\\ \text{so at x=-4 the denominator is equal to zero and thus \\x=-4 is excluded from the domain of f}$$

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Jul 12, 2019

#1
+6192
+1

The only values not in the domain are those that make the denominator zero.

Both terms are positive so they must both simultaneously be zero.

$$x^2 + 3x-4 = (x+4)(x-1)\\ x^2+9x+20 = (x+4)(x+5)\\ \text{so at x=-4 the denominator is equal to zero and thus \\x=-4 is excluded from the domain of f}$$

Rom Jul 12, 2019