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

f (x) = \frac{( x - 2 )}{x ^{2} - 16}

f (x) = ln (- 2 x^{2} - 2 x + 40)

f (x) = ln (26 - 9 x^{2})

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

f (x) = \frac{x}{x ^{2} + 12 x + 35}

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