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

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

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

domain

y = \frac{4 - x ^{2}}{x ^{2} - 1}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 2

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

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

f (x) = \frac{2 x}{16 - x ^{2}}

f (x) = 4 e^{x}

f (x) = ∣ x + 2 ∣ - 1

f (x) = \frac{6 x}{x ^{2} + 1}

(6, 19.1), (7, 19.8)

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