What is the domain of f(x)= 1/(9x^2+69x+130) ?

The domain of f(x)= 1/(9x^2+69x+130) is x -10/3

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domain of f(x)= 1/(9x^2+69x+130)

domain

f (x) = \frac{1}{9 x ^{2} + 69 x + 130}

x < - \frac{13}{3} or - \frac{13}{3} < x < - \frac{10}{3} or x > - \frac{10}{3}

Interval Notation

(- \infty, - \frac{13}{3}) \cup (- \frac{13}{3}, - \frac{10}{3}) \cup (- \frac{10}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{10}{3}, x = - \frac{13}{3}

The function domain

x < - \frac{13}{3} or - \frac{13}{3} < x < - \frac{10}{3} or x > - \frac{10}{3}

f (x) = lo g_{3} (2 + 6 x)

f (x) = \frac{x}{x ^{2} + 6}

\frac{x + 6}{x ^{2} - 4}

3^{x} + 2

\frac{4}{1 - 3 ( \frac{1}{x} )}

What is the domain of f(x)= 1/(9x^2+69x+130) ?
The domain of f(x)= 1/(9x^2+69x+130) is x<-13/3 \lor-13/3 <x<-10/3 \lor x>-10/3