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

The domain of (sqrt(x))/(2x-1)-1 is 0 1/2

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

domain

\frac{x}{2 x - 1} - 1

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

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

lo g_{2} (y + 5) + 3

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

f (y) = \frac{4 - y ^{2}}{1}

f (x) = - e - x + 4

\frac{3}{x ^{2} - 2 x - 3}

What is the domain of (sqrt(x))/(2x-1)-1 ?
The domain of (sqrt(x))/(2x-1)-1 is 0<= x< 1/2 \lor x> 1/2