What is the domain of f(x)=(5x+14)/(6x^2+x-2) ?

The domain of f(x)=(5x+14)/(6x^2+x-2) is x 1/2

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domain of f(x)=(5x+14)/(6x^2+x-2)

domain

f (x) = \frac{5 x + 14}{6 x ^{2} + x - 2}

x < - \frac{2}{3} or - \frac{2}{3} < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{2}{3}) \cup (- \frac{2}{3}, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{1}{2}, x = - \frac{2}{3}

The function domain

x < - \frac{2}{3} or - \frac{2}{3} < x < \frac{1}{2} or x > \frac{1}{2}

f (x) = \frac{x + 9}{x ^{2} - 49}

\frac{3}{3 x + 2 - 3 x - 2}

f (x) = 1 - \frac{∣ x + 1 ∣}{∣ x - 1 ∣}

f (x) = \frac{22}{4 x - 15}

f (x) = \frac{x - 8}{x ^{2} + 8 x - 9}

What is the domain of f(x)=(5x+14)/(6x^2+x-2) ?
The domain of f(x)=(5x+14)/(6x^2+x-2) is x<-2/3 \lor-2/3 <x< 1/2 \lor x> 1/2