What is the domain of sqrt((1-3x)/(x-1)) ?

The domain of sqrt((1-3x)/(x-1)) is 1/3 <= x<1

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domain of sqrt((1-3x)/(x-1))

domain

\frac{1 - 3 x}{x - 1}

\frac{1}{3} \leq x < 1

Interval Notation

[\frac{1}{3}, 1)

Solution steps

Find non-negative values for radicals:

\frac{1}{3} \leq x < 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

\frac{1}{3} \leq x < 1

f (x) = lo g_{3} (4 x - 5)

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

x^{2} + 2 x

\frac{2 x + 6}{- 6 x + 3}

f (x) = lo g_{10} (9 - x)

What is the domain of sqrt((1-3x)/(x-1)) ?
The domain of sqrt((1-3x)/(x-1)) is 1/3 <= x<1