What is the domain of f(x)= x/(ln(1-x)) ?

The domain of f(x)= x/(ln(1-x)) is x<0\lor 0<x<1

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domain of f(x)= x/(ln(1-x))

domain

f (x) = \frac{x}{ln ( 1 - x )}

x < 0 or 0 < x < 1

Interval Notation

(- \infty, 0) \cup (0, 1)

Solution steps

Find positive values for logs:

x < 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < 1

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

f (x) = 5 x - 4

f (x) = lo g_{10} (6 x^{2} - 13 x - 28)

f (x) = \frac{8 x ^{2} + 12 x}{9 x ^{2} - 12 x + 4}

g (t) = 2 t - 1

What is the domain of f(x)= x/(ln(1-x)) ?
The domain of f(x)= x/(ln(1-x)) is x<0\lor 0<x<1