What is the domain of y=(-8x^3sqrt(x+2))/(ln(-3x+1)) ?

The domain of y=(-8x^3sqrt(x+2))/(ln(-3x+1)) is -2<= x<0\lor 0<x< 1/3

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domain of y=(-8x^3sqrt(x+2))/(ln(-3x+1))

domain

y = \frac{- 8 x ^{3} x + 2}{ln ( - 3 x + 1 )}

- 2 \leq x < 0 or 0 < x < \frac{1}{3}

Interval Notation

[- 2, 0) \cup (0, \frac{1}{3})

Solution steps

Find non-negative values for radicals:

x \geq - 2

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

- 2 \leq x < 0 or 0 < x < \frac{1}{3}

y = \frac{- 2 - 9 x}{x - 7}

lo g_{2} (x + 1) - 2

f (x) = lo g_{x} (1 - e^{1 - x})

\frac{( x ^{2} - 6 x - 55 )}{x ^{2} - 3 x - 28}

f (x) = \frac{x ^{2} + 5 x}{x ^{3} - 13 x ^{2} + 36 x}

What is the domain of y=(-8x^3sqrt(x+2))/(ln(-3x+1)) ?
The domain of y=(-8x^3sqrt(x+2))/(ln(-3x+1)) is -2<= x<0\lor 0<x< 1/3