What is the domain of 1/(x+8)+ln(1/x-1/(1-x)) ?

The domain of 1/(x+8)+ln(1/x-1/(1-x)) is 0 1

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domain of 1/(x+8)+ln(1/x-1/(1-x))

domain

\frac{1}{x + 8} + ln (\frac{1}{x} - \frac{1}{1 - x})

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

Interval Notation

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

Solution steps

Find positive values for logs:

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

Find undefined (singularity) points:

x = - 8, x = 0, x = 1

Combine real regions and undefined points for final function domain

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

f (x) = 9 - x^{2}

f (x) = \frac{x ^{2} + x - 12}{x ^{2} - 4}

f (x) = - 1 + 7 x^{5}

f (x) = 3 (x = 0)^{2} = 0

f (x) = \frac{x - 7}{x ^{2}}

What is the domain of 1/(x+8)+ln(1/x-1/(1-x)) ?
The domain of 1/(x+8)+ln(1/x-1/(1-x)) is 0<x< 1/2 \lor x>1