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

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

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

domain

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

x < - 3 or - 3 < x \leq 2

Interval Notation

(- \infty, - 3) \cup (- 3, 2]

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x \leq 2

\frac{x + 1}{3 - x}

- \frac{3}{5}

f (x) = \frac{x ^{2} - 5 x - 6}{x ^{2} - 3 x - 18}

\frac{x + 4}{- 2 x - 6}

f (x) = 2 x - 6

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