What is the domain of sqrt((-2+x)/(4x-1/4)+3) ?

The domain of sqrt((-2+x)/(4x-1/4)+3) is x = 11/52

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domain of sqrt((-2+x)/(4x-1/4)+3)

domain

\frac{- 2 + x}{4 x - \frac{1}{4}} + 3

x < \frac{1}{16} or x \geq \frac{11}{52}

Interval Notation

(- \infty, \frac{1}{16}) \cup [\frac{11}{52}, \infty)

Solution steps

Find non-negative values for radicals:

x < \frac{1}{16} or x \geq \frac{11}{52}

Find undefined (singularity) points:

x = \frac{1}{16}

Combine real regions and undefined points for final function domain

x < \frac{1}{16} or x \geq \frac{11}{52}

What is the domain of sqrt((-2+x)/(4x-1/4)+3) ?
The domain of sqrt((-2+x)/(4x-1/4)+3) is x< 1/16 \lor x>= 11/52