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

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

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

domain

f (x) = \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

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

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

f (x) = \frac{( 28 x + 7 )}{x ^{2}}

x^{2} - 144

4 x - x^{2}

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