Question

find the domain of the given function. enter the solution using interval notation.
$n(x)=\frac{9 + 2x}{9x^{2}+11x - 14}$
domain:
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Explanation:

Step1: Find values that make denominator 0

Set $9x^{2}+11x - 14=0$.

Step2: Factor the quadratic equation

$(9x - 7)(x + 2)=0$.

Step3: Solve for x

$9x-7 = 0$ gives $x=\frac{7}{9}$; $x + 2=0$ gives $x=-2$.

Step4: Determine the domain

The domain is all real numbers except $x=-2$ and $x=\frac{7}{9}$. In interval - notation, it is $(-\infty,-2)\cup(-2,\frac{7}{9})\cup(\frac{7}{9},\infty)$.

Answer:

$(-\infty,-2)\cup(-2,\frac{7}{9})\cup(\frac{7}{9},\infty)$