What is the domain of f(x)=(x-2)/(3(x^2-1)-8x) ?

The domain of f(x)=(x-2)/(3(x^2-1)-8x) is x 3

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domain of f(x)=(x-2)/(3(x^2-1)-8x)

domain

f (x) = \frac{x - 2}{3 ( x ^{2} - 1 ) - 8 x}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

g (x) = ln (5 - x)

g (x) = \frac{1}{x - 1}

7 x^{2} - 12 x + 21

f (x) = arcsin (e^{3 x})

y = \frac{x ^{2} - 9}{x ^{2} + 2 x - 8}

What is the domain of f(x)=(x-2)/(3(x^2-1)-8x) ?
The domain of f(x)=(x-2)/(3(x^2-1)-8x) is x<-1/3 \lor-1/3 <x<3\lor x>3