What is the domain of (x+4x^3)/(x^2-2x^3) ?

The domain of (x+4x^3)/(x^2-2x^3) is x 1/2

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domain of (x+4x^3)/(x^2-2x^3)

domain

\frac{x + 4 x ^{3}}{x ^{2} - 2 x ^{3}}

x < 0 or 0 < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 0, x = \frac{1}{2}

The function domain

x < 0 or 0 < x < \frac{1}{2} or x > \frac{1}{2}

ln (x - x^{2} + 1)

f (x) = x^{2} - 4 - 4 x - x^{2}

f (x) = 9 x

h (x) = 27 - 9 x

What is the domain of (x+4x^3)/(x^2-2x^3) ?
The domain of (x+4x^3)/(x^2-2x^3) is x<0\lor 0<x< 1/2 \lor x> 1/2