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

The domain of f(x)=sqrt(|(x-1)/(x+2)|-2) is -5<= x<-2\lor-2<x<=-1

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

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

f (x) = \frac{1}{2} x - 8

x (4 - 3 x)

0.8413

\frac{7 x}{2 x + 9}

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

What is the domain of f(x)=sqrt(|(x-1)/(x+2)|-2) ?
The domain of f(x)=sqrt(|(x-1)/(x+2)|-2) is -5<= x<-2\lor-2<x<=-1