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

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

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

domain

\frac{x}{( 3 - x ) ( x + 2 )}

x < - 2 or 0 \leq x < 3

Interval Notation

(- \infty, - 2) \cup [0, 3)

Solution steps

Find non-negative values for radicals:

x < - 2 or 0 \leq x < 3

Find undefined (singularity) points:

x = 3, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or 0 \leq x < 3

f (x) = (x - 3)^{2} - (x - 8)^{2}

18 x - 9 x^{2} - 9

f (x) = 5 x^{2} - 4 y^{2} - 20 = 0

f (x) = \frac{1 + x}{9 - x}

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