What is the domain of f(x)=(2x)/(3x^2-13x-10) ?

The domain of f(x)=(2x)/(3x^2-13x-10) is x 5

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domain of f(x)=(2x)/(3x^2-13x-10)

domain

f (x) = \frac{2 x}{3 x ^{2} - 13 x - 10}

x < - \frac{2}{3} or - \frac{2}{3} < x < 5 or x > 5

Interval Notation

(- \infty, - \frac{2}{3}) \cup (- \frac{2}{3}, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5, x = - \frac{2}{3}

The function domain

x < - \frac{2}{3} or - \frac{2}{3} < x < 5 or x > 5

\frac{x}{x ^{2} - 5 x + 4}

f (x) = \frac{5 x}{100 - x}

2^{s i n (x)}

f (x) = \frac{3 ( x - 2 )}{x ^{2} - 4}

f (x) = (x - 2)^{2} (x - 1)

What is the domain of f(x)=(2x)/(3x^2-13x-10) ?
The domain of f(x)=(2x)/(3x^2-13x-10) is x<-2/3 \lor-2/3 <x<5\lor x>5