What is the domain of g(x)=(sqrt(2x-1))/(x-5) ?

The domain of g(x)=(sqrt(2x-1))/(x-5) is 1/2 5

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domain of g(x)=(sqrt(2x-1))/(x-5)

domain

\frac{1}{2} \leq x < 5 or x > 5

Interval Notation

[\frac{1}{2}, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{2}

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

\frac{1}{2} \leq x < 5 or x > 5

What is the domain of g(x)=(sqrt(2x-1))/(x-5) ?
The domain of g(x)=(sqrt(2x-1))/(x-5) is 1/2 <= x<5\lor x>5