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

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

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

domain

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

x \leq - \frac{3}{4} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{3}{4}] \cup (\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{3}{4} or x > \frac{1}{2}

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

x \leq - \frac{3}{4} or x > \frac{1}{2}

f (x) = \frac{x}{x ^{2} - 5}

f (x) = - 2 x^{2} + 12 x + 5

f (x) = \frac{5}{x ^{2} - x}

f (x) = - 3 t

f (x) = lo g_{2} (x - 3) + 1

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