What is the domain of (-8x\sqrt[3]{x+2})/(ln(-3x+1)) ?

The domain of (-8x\sqrt[3]{x+2})/(ln(-3x+1)) is x<0\lor 0<x< 1/3

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domain of (-8x\sqrt[3]{x+2})/(ln(-3x+1))

domain

x < 0 or 0 < x < \frac{1}{3}

Solution steps

Find positive values for logs:

x < \frac{1}{3}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < \frac{1}{3}

\frac{x - 6}{x ^{2} - 3 x - 18}

\frac{2 x ^{2} + 4 x - 6}{4 x ^{2} + 16 x + 12}

f (x) = lo g_{\frac{1}{5}} (x^{2} - x - 12)

\frac{x - 9}{x ^{2} - 81}

f (x) = tan (x) - 3

What is the domain of (-8x\sqrt[3]{x+2})/(ln(-3x+1)) ?
The domain of (-8x\sqrt[3]{x+2})/(ln(-3x+1)) is x<0\lor 0<x< 1/3