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

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

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

domain

\frac{x - 2}{( x + 3 ) 1 - x}

x < - 3 or - 3 < x < 1

Interval Notation

(- \infty, - 3) \cup (- 3, 1)

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = - 3, x = 1

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x < 1

6 - \frac{6 y + 7 x}{2} = 1

- x^{3} + 3 x^{2} - 1

f (x) = x^{2} - x - 6

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

f (x) = 2 x

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