What is the domain of f(x)=(sqrt(4-x^2)-1)/(1-|x-2|) ?

The domain of f(x)=(sqrt(4-x^2)-1)/(1-|x-2|) is -2<= x<1\lor 1<x<= 2

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domain of f(x)=(sqrt(4-x^2)-1)/(1-|x-2|)

domain

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

- 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, x = 3

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=(sqrt(4-x^2)-1)/(1-|x-2|) ?
The domain of f(x)=(sqrt(4-x^2)-1)/(1-|x-2|) is -2<= x<1\lor 1<x<= 2