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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 2

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

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

f (x) = 2 t + t^{2}

ln (x^{2} + 5 x - 6)

\frac{x ^{2}}{x ^{2} - x - 6}

f (x) = \frac{5}{3 - x}

f (x) = \frac{17}{x - 6}

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