What is the domain of sqrt((4x+3)/(2x+5)) ?

The domain of sqrt((4x+3)/(2x+5)) is x =-3/4

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domain of sqrt((4x+3)/(2x+5))

domain

\frac{4 x + 3}{2 x + 5}

x < - \frac{5}{2} or x \geq - \frac{3}{4}

Interval Notation

(- \infty, - \frac{5}{2}) \cup [- \frac{3}{4}, \infty)

Solution steps

Find non-negative values for radicals:

x < - \frac{5}{2} or x \geq - \frac{3}{4}

Find undefined (singularity) points:

x = - \frac{5}{2}

Combine real regions and undefined points for final function domain

x < - \frac{5}{2} or x \geq - \frac{3}{4}

f (x) = x^{3} - 6 x^{2} + 9 x + 5

\frac{x ^{2} - 6 x + 8}{x ^{2} - 16}

f (n) = \frac{1}{9} n - \frac{4}{9}

f (x) = 2 x^{3} - 3 x^{2} - 36 x

f (x) = 3 x + 3

What is the domain of sqrt((4x+3)/(2x+5)) ?
The domain of sqrt((4x+3)/(2x+5)) is x<-5/2 \lor x>=-3/4