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

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

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

domain

f (x) = \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

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