What is the domain of y=sqrt(((2x-1))/(1-3x)) ?

The domain of y=sqrt(((2x-1))/(1-3x)) is 1/3 <x<= 1/2

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domain of y=sqrt(((2x-1))/(1-3x))

domain

y = \frac{( 2 x - 1 )}{1 - 3 x}

\frac{1}{3} < x \leq \frac{1}{2}

Interval Notation

(\frac{1}{3}, \frac{1}{2}]

Solution steps

Find non-negative values for radicals:

\frac{1}{3} < x \leq \frac{1}{2}

Find undefined (singularity) points:

x = \frac{1}{3}

Combine real regions and undefined points for final function domain

\frac{1}{3} < x \leq \frac{1}{2}

f (x) = \frac{3}{8} x

f (x) = 1 + cos (x)

7 x^{2} + 1

f (x) = - 3 x^{2} + 7

f (x) = 2 x^{4} + 4 x^{3} + 2 x^{2}

What is the domain of y=sqrt(((2x-1))/(1-3x)) ?
The domain of y=sqrt(((2x-1))/(1-3x)) is 1/3 <x<= 1/2