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

The domain of y=sqrt(|(2x-3)/(2x+3)|-1) is x<-3/2 \lor-3/2 <x<= 0

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domain of y=sqrt(|(2x-3)/(2x+3)|-1)

domain

y = \frac{2 x - 3}{2 x + 3} - 1

x < - \frac{3}{2} or - \frac{3}{2} < x \leq 0

Interval Notation

(- \infty, - \frac{3}{2}) \cup (- \frac{3}{2}, 0]

Solution steps

Find non-negative values for radicals:

x < - \frac{3}{2} or - \frac{3}{2} < x \leq 0

Find undefined (singularity) points:

x = - \frac{3}{2}

Combine real regions and undefined points for final function domain

x < - \frac{3}{2} or - \frac{3}{2} < x \leq 0

\frac{100}{x ^{2}} - 9

r (x) = \frac{x ^{2} + 5 x}{25 - x ^{2}}

- e^{x} - 6

1 - cy

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

What is the domain of y=sqrt(|(2x-3)/(2x+3)|-1) ?
The domain of y=sqrt(|(2x-3)/(2x+3)|-1) is x<-3/2 \lor-3/2 <x<= 0