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

The domain of f(x)=(ln(1-x))/(sqrt(x^3+2x)) is 0<x<1

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

domain

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

0 < x < 1

Solution steps

Find non-negative values for radicals:

x \geq 0

Find positive values for logs:

x < 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

0 < x < 1

- x + 6

y = x^{2} - 2 x - 1

5 x - 10

f (x) = \frac{x + 4}{x ^{2} - 5 x + 6}

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