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

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

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

domain

g (x) = \frac{1 - x}{x + 2}

x < - 2 or - 2 < x \leq 1

Interval Notation

(- \infty, - 2) \cup (- 2, 1]

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x \leq 1

f (x) = 4 x + 1

y = \frac{x}{x - 1}

f (x) = x^{2} - x + 6 + 1, - 1 \leq x < 4

\frac{x - 4}{x ^{2} + 9}

tan (t)

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