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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

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

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

- 3 x - 1

\frac{5 x}{7 x - 2}

f (x) = \frac{x ^{2} - 4 x + 3}{x ^{2} - 1}

x^{2} + 16

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