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

The domain of f(x)=(sqrt(2x-1))/(1-x) is 1/2 1

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domain of f(x)=(sqrt(2x-1))/(1-x)

domain

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

\frac{1}{2} \leq x < 1 or x > 1

Interval Notation

[\frac{1}{2}, 1) \cup (1, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{2}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

\frac{1}{2} \leq x < 1 or x > 1

What is the domain of f(x)=(sqrt(2x-1))/(1-x) ?
The domain of f(x)=(sqrt(2x-1))/(1-x) is 1/2 <= x<1\lor x>1