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

Guest Jul 12, 2019

#1**+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

#1**+1 **

Best Answer

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